Graph G(x)=(x-1)^2 - Mathway

Enter a problem... Algebra Examples Popular Problems Algebra Graph g(x)=(x-1)^2 Step 1Find the properties of the given parabola.Tap for more steps...Step 1.1Use the vertex form, , to determine the values of , , and .Step 1.2Since the value of is positive, the parabola opens up.Opens UpStep 1.3Find the vertex .Step 1.4Find , the distance from the vertex to the focus.Tap for more steps...Step 1.4.1Find the distance from the vertex to a focus of the parabola by using the following formula.Step 1.4.2Substitute the value of into the formula.Step 1.4.3Cancel the common factor of .Tap for more steps...Step 1.4.3.1Cancel the common factor.Step 1.4.3.2Rewrite the expression.Step 1.5Find the focus.Tap for more steps...Step 1.5.1The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.Step 1.5.2Substitute the known values of , , and into the formula and simplify.Step 1.6Find the axis of symmetry by finding the line that passes through the vertex and the focus.Step 1.7Find the directrix.Tap for more steps...Step 1.7.1The directrix of a parabola is the horizontal line found by subtracting from the y-coordinate of the vertex if the parabola opens up or down.Step 1.7.2Substitute the known values of and into the formula and simplify.Step 1.8Use the properties of the parabola to analyze and graph the parabola.Direction: Opens UpVertex: Focus: Axis of Symmetry: Directrix: Direction: Opens UpVertex: Focus: Axis of Symmetry: Directrix: Step 2Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.Tap for more steps...Step 2.1Replace the variable with in the expression.Step 2.2Simplify the result.Tap for more steps...Step 2.2.1Simplify each term.Tap for more steps...Step 2.2.1.1Raising to any positive power yields .Step 2.2.1.2Multiply by .Step 2.2.2Simplify by adding numbers.Tap for more steps...Step 2.2.2.1Add and .Step 2.2.2.2Add and .Step 2.2.3The final answer is .Step 2.3The value at is .Step 2.4Replace the variable with in the expression.Step 2.5Simplify the result.Tap for more steps...Step 2.5.1Simplify each term.Tap for more steps...Step 2.5.1.1Raise to the power of .Step 2.5.1.2Multiply by .Step 2.5.2Simplify by adding numbers.Tap for more steps...Step 2.5.2.1Add and .Step 2.5.2.2Add and .Step 2.5.3The final answer is .Step 2.6The value at is .Step 2.7Replace the variable with in the expression.Step 2.8Simplify the result.Tap for more steps...Step 2.8.1Simplify each term.Tap for more steps...Step 2.8.1.1Raise to the power of .Step 2.8.1.2Multiply by .Step 2.8.2Simplify by adding and subtracting.Tap for more steps...Step 2.8.2.1Subtract from .Step 2.8.2.2Add and .Step 2.8.3The final answer is .Step 2.9The value at is .Step 2.10Replace the variable with in the expression.Step 2.11Simplify the result.Tap for more steps...Step 2.11.1Simplify each term.Tap for more steps...Step 2.11.1.1Raise to the power of .Step 2.11.1.2Multiply by .Step 2.11.2Simplify by adding and subtracting.Tap for more steps...Step 2.11.2.1Subtract from .Step 2.11.2.2Add and .Step 2.11.3The final answer is .Step 2.12The value at is .Step 2.13Graph the parabola using its properties and the selected points.Step 3Graph the parabola using its properties and the selected points.Direction: Opens UpVertex: Focus: Axis of Symmetry: Directrix: Step 4

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