Practice Quadratic Vertex Form in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A quadratic written as f(x)=a(x−h)2+k, where the vertex (h,k) is directly readable from the formula.

Imagine sliding a basic x2 parabola around on the coordinate plane. The value h shifts it left or right, k shifts it up or down, and a stretches or flips it. The vertex (h,k) is the parabola's turning point—you can read it directly from this form.

Showing a random 20 of 50 problems.

Example 1

medium
Convert f(x)=x2+6x+13 to vertex form.

Example 2

medium
Convert f(x)=2x2−12x+7 to vertex form.

Example 3

easy
What is the vertex of g(x)=−3(x+1)2+6?

Example 4

easy
Find the vertex of y=(x−3)2+4.

Example 5

easy
What is the vertex of g(x)=−(x+5)2−2?

Example 6

medium
Find the vertex of y=−(x−2)2.

Example 7

challenge
Find k so that y=(x−2)2+k is tangent to the x-axis.

Example 8

easy
Find the axis of symmetry of y=(x+4)2+1.

Example 9

medium
For y=−(x+4)2+3, what are the maximum value and where it occurs?

Example 10

easy
What is the vertex of f(x)=(x−7)2+2?

Example 11

easy
Find the maximum value of y=−2(x+3)2+8.

Example 12

medium
Convert f(x)=x2−8x+11 to vertex form by completing the square.

Example 13

easy
Does y=(x−1)2+3 open up or down?

Example 14

medium
Write the vertex form of a parabola with vertex (−1,4) passing through (0,7).

Example 15

medium
Translate the parabola y=x2 right 3 units and down 4 units. Write the vertex form.

Example 16

challenge
A ball's height is h=−16t2+64t. Write in vertex form and give the maximum height.

Example 17

hard
A ball's height in metres is h(t)=−5(t−2)2+25 where t is seconds. What is the maximum height and when?

Example 18

medium
A parabola has vertex (0,5) and passes through (2,1). Find its vertex-form equation.

Example 19

easy
Write the vertex form of a parabola with vertex (2,−3) and a=1.

Example 20

medium
A parabola has vertex (2,−1) and passes through (0,3). Find a in vertex form.