WHAT IS THE QUADRATIC PARENT FUNCTION AND HOW CAN ...

WHAT IS THE QUADRATIC PARENT FUNCTION AND HOW CAN YOU RECOGNIZE THE KEY FEATURES OF ITS GRAPH?

5/3/2019

69 Comments

1. The graph F(x)=/x/ is similar to the F(x)=x^2 because they all are in a curved shape and their y-intercept is zero, which is the origin. Plus the half of the side is the reflection of the other side. Both graph the two lines does not cross because it is very wide. The first quadratic functions in a v-shape and the second one is in a u-shape. The first one is wider than the second one. 2. The first graph and the second is cut in half in the middle of the order pair (0,0). When you cut it in half then you could see both graph one of the side is always the reflection of the other side.

Hi Jane, I'm Alexander from 816. I disagree with your compare and contrast. They are actually parent functions. And both have the symetery of x=0. Everything else was good explanatory.

I agree with every thing you said and want to add that they are both quadratic functions and that the vertex is (0,0)

Hi Jane, I'm Alexander from 816. I disagree with your compare and contrast. They are actually parent functions. And both have the symetery of x=0. Everything else was good explanatory.

1) These two functions are both quadratic and are called parent quadratic functions. Both have the vertex of the (0,0). One is the absolute value function and is in a V-shape. The second is an exponential function and is in a U-shape form. 2) Both have the symmetry line as x=0 or the y-axis. And it concludes that both are their own parabolas. It also shows that These functions are not shifted, nor translated anywhere.

Hi Alex Lempert, I think the second function F(x)=x^2 is not an exponential function. I think it is a quadratic function because it is in second degree. Exponential function is when x is the exponent.

Hello Alex from 816. i would like to agree with your statements about both functions, however, next time go into more detail about how the quadratic function differs from other functions.

1.Both graphs are similar by being quadratic functions,have the vertex as (0,0),and both facing upwards.The graphs differ by the first graph is a V shape while the second graph is a U shape. 2.I notice that the axis of each graph is x=0.

Hello Daria! I agree with your answer and you explained it nice and clearly for the first question. As for the second one, I think there needs to be more explanation.

1. Both graphs are similar because both graphs didn't go beyond (0,0). Also both graphs has lines going in both direction ( left and right). The difference of the two graphs is that one is curved and the other is straight. 2. Both graph's line of symmetry are 0,0 that means both graphs are parent function.

Hi Youlin, I'm Ekaterina from 816. I completely agree with everything that you said, but i would like to add on that both of these functions go upward so that means that they have only positive numbers. Also, the second one has an exponent but the first one does not.

A. The graphs are similar because the both go in the upward direction, so all of the numbers are positive. Also, their y -intercept/vertex is (0,0) and they are both parent functions. The differences are that the second one has an exponent but the first one does not. In addition, they are different shapes; the first one is in a V- shape and the second one has a U- shape. B. The axis of symmetry in each graph is the same, it is both (0,0). It goes through the y-axis or x=0 for both of them.

Hi Ekaterina, I agree with your explanation and I would like to add on that, you could also say that both parabola are symmetrical shape since when the x-axis is 0<x and x>0 they are a reflection of each other.

1) F(x)=x^2 and F(x)=/x/ are parent function. The difference is that F(x)=/x/ is an absolute function that graphed into a v-shape and F(x)=x^2 graphed into a U-shape. 2) The line of symmetric for both function is x=0.

Hi Cecelia, I agree with your answer, especially about how f(x)=/x/ is an absolute function which graphs into a v shape. I think you should work on providing more similarities and differences, because I think there are more. :D

a. The graph of f(x)=/x/ is similar to f(x)=x^2 because f(x)=/x/ is the parent function, and that they are both symmetrical. Both quadratic equations are non-linear because they do not have a straight line, and their vertex are the same. The two functions are different because the graph of f(x)=/x/ is different to the graph of f(x)=x^2. b. The two functions both form a line of symmetry from (0,0) because both functions on the graph has a point where they hit (0,0) and if you reflect, you can see that they are both symmetrical.

Hi Elaine, I'm Amy from 815 , I agree with your explanation but I think you should provide examples on how each graphs are different.

1) Differences and similarities: Differences: ~ The function f(x) = |x| * has 2 straight symmetric lines along the y-axis. * an absolute function. ~ The function f(x) = x^2 * has 2 curved symmetric lines along the y-axis. * 2nd degree function Similarities: * Both have a minimum point at (0,0) also it's the vertex. * Both are symmetric parabola * Does not cross the x-axis. 2) The axis of symmetry for both function is the y-axis or x=0.

Hi Amy, I'm Ying Ping from 815, I agree with you on both answer to the question because the similarities and differences are most likely what i wrote too. As for the second answer, I agree with you too but you can maybe add a little more details.

1. They graphs are similar because both of there y-intersepts are 0. The differences are the first graph is in a v shape because it is absolute value. The second graph is in a u shape because it has a exponent. 2.both graphs are parent functions because the graphs line of symmetry line is (0,0 )

1) both graphs at (0,0) they both are positive . The difference is that the line f(x) = |x| is a graph with a absolute value which forms a “v” shape. 2) one thing I noticed is that x=0

Greetings Kamila Aslamova from class 816, I am Jessica Z from class 815 I understand what you are trying to say, and it is correct. However, next time you can maybe add more vocabulary and as Ms.Alighieri says " you are algebra 1 students, you should speak like one, not like a fifth grader.".

1) Similarity/ies: -they are both the parent function (meaning that there would be a couple of similarities, which include same origin. both are symmetrical, same line of symmetry,both do not cross the x-axis, etc.) ---------------------------------------------------------------------------------------- Differences: -one is a absolute function (meaning it forms a v when graphed) -the other one is a quadratic function (meaning it forms a u when graphed) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 2) I notice that they are both the same (x=0).

Hi Jessica, I agree with you on your statements and I like your similarities and differences.

A. Both graphs represent a quadratic parent function even though one looks a little different than the other. Some similarities is that both graphs have a vertex of (0,0) and they both have positive coordinates. Some differences is that they graph into different shapes, one into a "v" and another into a "u". B.The axis of symmetry is the same for both of them, its (0,0). It goes through the y-axes for both of them.

Hi Kateryna, I 'm Ngaying from 815. I agree with your answer about the similarity and the differences of the functions and I like how you explain about the axis of symmetry.

A) Relationship Similarities: The graph f(x)=lxl and f(x)=x^2 is similar to each other by ~Both from function family ~Non-linear ~Parent function ~Vertex could be (0,0) Difference: The graph f(x)=lxl and f(x)=x^2 is difference to each other by ~f(x)=x^2 is the quadratic function and f(x)=lxl is the absolute value function ~f(x)=x^2 is curved and f(x)=lxl is the not curved but a line that splits the function into equal and opposite 'halves' B) The axis of symmetry for the graph f(x)=lxl is x=0 and f(x)=x^2 is x=0. Shown in the graphs has the vertex of (0,0).

hi ying ping I like your answer it was very detailed and you examples everything very well I like how you explained how the both graphs are similar

1. The graph of f(x)=|x| and f(x)=x^2 are Similar: -vertex (0,0) -line of symmetry x=0 -Doesn't go below zero -are both parent functions -Both non linear Differences: ~f(x)=|x| ~f(x)=x^2 -make V shape -makes U shape -wider -less wider -absolute -quadratic 2. I notice both of the axis on the 2 graph are on (0,0). Which is the symmetry is x=0

Hi Ying, I'm Selina. I totally agree with you about the similarities and differences. I like how you gave many examples. Good.

I agree with you, i liked how you put a lot of information about the similarities and differences.

A. The graph of f(x) = /x/ similar to the graph of f(x) = x^2 by they both have the same minimum of 0 and a same vertex(0,0), they are form the fraction family, and they are going to the same direction. The differences are the graph of f(x) = /x/ is a V shape and the graph of f(x) = x^2 is a U shape, and the graph of f(x) = /x/ is wider than the graph of f(x)= x^2. B. The axis of symmetry of both graph is the same, so the axis of symmetry of both graph is x = 0.

A. The graph of f(x)= lxl and f(x)= x^2 are similar because both have the vertex of (0,0). Both are symmetrical and both are the parent functions. Goes in one direction and both non-linear. The graphs are different because f(x)= lxl is a V-shape parabola while f(x)= x^2 is a U-shaped parabola. One graph is absolute value function while the other one is a quadratic function. f(x)= lxl is more wider than f(x)=x^2. B. I noticed that the axis of symmetry of both graphs are the same. the axis of symmetry is the y-axis or x=0.

1. The graph F(x)=/x/ is similar to F(x)=x^2 because they have the same parent function, they both curve and they both their y-intercepts are both zero. The first quadratic function asks to find the absolute value of x and the second quadratic function asks to square x. The first quadratic function is in the shape fo a V and the second quadratic function is in the shape of a U. 2. 2. For both graphs, the line of symmetry is at the point (0,0) because it is in the middle. Also, it is the minimum value of both graphs.

Hi Daniela from 816, I agree with your answers and understand your reasoning but to strengthen your claim, you could've provided a few more similarities and differences. Also, for your response to the second question your did not mention anything about the axis.

1. The two graphs are both non-linear and are parent quadratic functions since both have a vertex of (0,0)The two graphs similarities are they both have a line of symmetry and they share identical lines of symmetry which is x=0. They also share the same y-int which is the origin(0,0). The graphs are also positive. Domains and Ranges are also identical. Differences the two graphs one is a u shape and the other is a v shape. One is an absolute value while the other is an exponential parabola. 2. Both graphs share the exact same line of symmetry at the point (0,0) or the origin. The line of symmetry is found on the y axis and can be graphed as x=0.

Hi Daniel I am Derrick from 81 and I think you did very well explaining your answer. Your answer contains not only the right answer but a perfect explanation to go along with it as well. Good Job

The two graphs are both the parent functions of its own category. The V shaped graph is the parent function of a absolute value function while the U shaped graph is the parent function of the quadratic function. The similarities are that both lines are linear and go through the origin. Both lines have their lines of symmetry at x=0 and share the same vertex at (o,o). I noticed that both lines had the same line of symmetry which goes to the origin. The point is on the y axis and the equation for it is x=0.

Hi derek, I agree with your explaination and I like how you described the absolute value of a function.

1. The two graphs have a vertex of (0,0). One of the functions graphs into a u shape while the other one graphs into a v shape. 2.The line of symmetry is (0,0) the value is also a-min.

I agree with most of what u said, but i would like to say that the line of symmetry is a line, not a point.

I agree with you but I think you should explain your answer a bit more and go into more detail with your explanation.Also as WenJia said your line pf symmetry should not be a point.

The parent function of a quadratic function is f(x) = x^2, and some of its key features are: 1) The line of symmetry is the y-axis. 2) Vertex is at (0,0). 3) Slope is NOT constant. 4) Graph is a U-shape curve. It's similar to the graph of f(x)=|x| in a way that both of them shares the line of symmetry of x=0, and the vertex is both (0,0). They are also the parent functions of quadratic equation and absolute value equation respectively. They are different, because f(x)=x^2 is a curve, and f(x)=|x| have straight lines.

I agree with your statement, but you forgot to explain about both equations having a minimum, and having the same domain and range.

The quadratic parent function is f(x) = x^2. To recognize key characteristics of the parent, is that, its in a U shape, or a parabola. Its vertex is (0,0) and the line of symmetry is x=0 or the y intercept. The domain of the parent function is all real numbers, while the range is y>0. If the function is f(x)=x^2+b their is a added value of b, which changes the vertex to (0,b) as its minimum is now the value of b. However all other values are the same, except that, since theirs a new minimum, the range is y is greater than or equal to b.

The graphs are similar because both of the graphs have a y intercept of (0,0).They also both fold upwards which means that they have a minimum.And both graphs have the min of 0. However there're also differences in these graphs.The first function graphs into a v which means that it is called an absolute value graph and the second function graphs into a u-shape. Both of the graphs and functions have the same line of symmetry which is x=0.

A. Both f(x) = |x| and f(x) = x^2 are similar because they will always get a positive y coordinate, a vertex of (0,0), the same y intercept and line of symmetry. However they are different because some of their coordinates are different from each other and they both form different shapes like f(x) = x^2 makes a upward U shape. B. I noticed that even though there graphs maybe different they still have the same line of symmetry and the line of symmetry fits even to the graph with an absolute value. In this case f(x) = x^2 will be the quadratic parent function because it is the only one making a U shape and has a leading coefficient. I can also recognize the key features by using equations.

Hi Tianlang, overall I agree with your response, but I feel like you should have explained part B a little bit better, like how both graphs have a line of symmetry on the y-axis.

1) The functions f(x)=|x| and f(x)=x^2 are similar because they are both non-liner and positive also have the same vertex of (0,0) the both functions are called quadratic functions. The function are different because the function f(x)=|x| is a v-shape and the function f(x)=x^2 is a u-shape 2) the line of symmetry is for both of the function is x=0

both graphs are similar because they are increasing and decreasing in equal intervals and are going through the origin. The graphs are also different because the first graph is made up of 2 linear functions and the second graph is not linear. both graphs have a y-axis as a line of symmetry.

A) the graphs are both similar because of the vertex, it is at the origin (0,0), also, these two graphs are positive. And also, another similarity they have is that they both are parent functions. B)The axis of symmetry are the same, it is x=0

Hi Nelly, im Elizabeth Plotkin from 816, I fully agree with your answer for these two questions.

Hello Nely, I am Madisen from 814. I fully agree with your statements, but I must add to your first answer, as you could have mentioned the similarities in their line of symmetry as another similarity.

a) the graph f(x)=[x] is similar to graph f(x)=x^2 because they have the same vertex also both are non-linear.They are different because they are different shape f(x)=[x] is a v shape and f(x)=x^2 is a u shape. b)The symmetry are both on the y-axis . Also both have the same vertex which makes them both have the same line of symmetry which is 0.

1.They are both quadratic functions and that the vertex is (0,0),both graphs are a min. The difference between these two graphs is that one is a U shape and one is a V shape.The reason one is a V and one is a U is because one is an absolute value and one is to the power of 2. 2.the line of symmetry is x=0

A: Both graphs have a min, as well as this they have vertexes located at (0,0),. They both open upwards and have the same line of symmetry B: The line of symmetry is x=0 for both of these graphs.

Both graphs have vertex’s located at (0,0) they both also have the same line of symmetry. In addition the graphs have a min. Both are quadratic functions. The difference is that one is a U shape and another is a V shape. Also the absolute values are different. These are the comparisons. :)

Hi Anastasia I completely agree with you though you should mention the important difference that one is a U shape and one is a V shape.

A. The graphs are similar because the numbers are positive so they go in the upwards directions. They are both parent functions and their vertex is (0,0). However the graphs are different shapes. The first one is a V- shape and the second one is a U- shape. B. The graphs have the same axis of symmetry which is (0,0). Also, they both go through x=0.

1. The graphs are similar because they both go up.Therefore, all of the numbers are positive numbers. Another way, the graphs are similar is because the y-intercept and vertex is at the origin (0,0). Both graphs are also parent functions. A difference is that one of the equations have an exponent and the other does not. One graph is U-shaped, while the second graph is V-shaped. B. The Axis of Symmetry for both graphs are at (0,0) the origin, and the y-intercept is also the line of symmetry.

1.The similarities is that both of these functions are quadratic and have a vertex which is located in (0,0), they are also both not linear. The differences is that function f(x)=/x/ forms into a v shape and function f(x)=x^2 forms into a u shape parabulla. 2.The line of symetry is on the y-axis and its x=0.

The parent function is identified as a standard parabola, the equation being y=x^2, it's vertex and only root being (0,0) and having x=0 as it's line of symmetry. a: Graphs y=IxI and y=x^2 are similar because they have repeating patterns on either side of the x-axis, which acts as the line of symmetry. On the other hand, they are different because y=x^2 is a parabola, and therefore is not linear or straight. y=IxI is straight on both sides and gives an illusion as if it was a linear graph yet reflected. b: On both graphs, the axis of symmetry is x=o, or the x-axis itself, as both lack a B, or something to manipulate horizontal shift.

Both graphs are similar because they both make a U-shape, therefore all of the numbers are positive. Also both of these functions are quadratic and have a vertex of (0, 0).both graphs are also parent functions , half of one side is the the same as the other. The difference between both graphs is one forms a U-shape and the other a v-shape, they have different range coordinates. 100%

The graph of F(x)=/x/ is similar to the graph F(x)=x^2 because both of quadratic functions are non-linear,since that are not straight lines. They can also be similar because they are both symmetrical, They have a vertex at (0,0) Both graphs are different because function F(x)= x^2 is raised to the second power, and is shaped like an upward umbrella. Function F(x)= /x/ is an absolute value, and has 2 symmetrical lines among the y-axis. I notice that the axis of symmetry fro both graphs is x=0

A)Both graphs have reflection over the y-axis. The graphs have a vertex at (0,0).And have a line of symmetry of x=0.Both are non-linear but still positive. But f(x)=|x| makes a V-shape or umbrella while F(x)=x^2 makes a U-shape B)That the y-axis is the line of reflection in both graphs

A: First off I notice that both graphs have a vertex of (0,0) also the fact that they both have a min. of 0, also that both graphs are positive. Yet one difference I see is that f(x)=x^2 is a positive parent function making it a U-shape while f(x)=IxI is a v-shaped graph and a absolute value function. B: Both of the graphs are symmetric on the y-axis

The graph F(x)=/x/ is similar to the F(x)=x^2 because they all are in a curved angle. both start at the origin (0,0) and are both positive if it was negative it would look like an umbrella and its facing up which means its positive. ---ALSO the line of symmetry IS X=0 they both have the same line of symmetry for both graphs which shows another reason why they similar

Hi Mike, I'm Sean from your class. I disagree with your statement on how they are similar. F(x)= |x| doesn't show a curve, it shows an edge. Quadratic functions have a curve but absolute values don't. One other thing that they have in common is that they are both parent functions. You need to also explain the differences.

A) One major thing both graphs have in common is that they are both parent functions. The top graph is the parent function for absolute value. The bottom graph is the parent function for quadratic function. The graphs both have the same axis of symmetry, x=0. They also have the same vertex, (0,0), or known as the origin. One more thing is that they both have a min and no max. The min for both is 0. One thing that is different is the appearance of the graph. F(x)= |x| is a V shape with an edge. F(x)= x^2 looks like a U shape with a curve. Another difference is the direction of the graph. The quadratic function gets straighter the more the y-coordinates increase. The absolute value function has two linear lines moving away from each other. It looks like two linear equations intersecting at a point. That is one way to tell them apart. B) I notice that they have the same axis of symmetry, simply the y-axis and/or x=0. Since that both graphs are represented by parent functions, they should have a lot of things in common. The axis of symmetry is one of them.

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