How Do You Draw F(x) = -2x^2 And G(x) = 2x-4 On The Same Graphs?

How do you draw #f(x) = -2x^2# and #g(x) = 2x-4# on the same graphs? Algebra

1 Answer

Jacq Oct 4, 2017

Explanation:

To draw these on the same graph, you first need to know what each graph looks like individually:

#f(x)=-2x^2# is an upside-down parabola: graph{-2x^2 [-20, 20, -10, 10]}

Due to the #2# in front of the #x^2#, the graph is steeper than a usual one. If you are unsure about how to convey the steepness, I recommend you sub in a point on the graph to see where it would be (e.g. #when# #x=2, y=-8#).

#g(x)=2x-4# is a linear equation (i.e. a straight line). This can be graphed by finding the x- and y-intercepts, and then drawing a line that goes through the points.

x-intercept (when y=0), #0=2x-4# #2x=4# #therefore x=2#

y-intercept (when x=0), #y=2(0)-4# #therefore y=-4#

graph{2x-4 [-40, 40, -20, 20]}

To graph these on the same graph, you need to make sure you have a common scale. These two equations graphed on the same axes look like this:

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