Practice Quadratic Vertex Form in Math

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

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Quick Recap

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

Imagine sliding a basic x2x^2 parabola around on the coordinate plane. The value hh shifts it left or right, kk shifts it up or down, and aa stretches or flips it. The vertex (h,k)(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+13f(x) = x^2 + 6x + 13 to vertex form.

Example 2

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

Example 3

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

Example 4

easy
Find the vertex of y=(x−3)2+4y = (x - 3)^2 + 4.

Example 5

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

Example 6

medium
Find the vertex of y=−(x−2)2y = -(x-2)^2.

Example 7

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

Example 8

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

Example 9

medium
For y=−(x+4)2+3y = -(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+2f(x) = (x-7)^2 + 2?

Example 11

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

Example 12

medium
Convert f(x)=x2−8x+11f(x) = x^2 - 8x + 11 to vertex form by completing the square.

Example 13

easy
Does y=(x−1)2+3y = (x-1)^2 + 3 open up or down?

Example 14

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

Example 15

medium
Translate the parabola y=x2y = x^2 right 33 units and down 44 units. Write the vertex form.

Example 16

challenge
A ball's height is h=−16t2+64th = -16t^2 + 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+25h(t) = -5(t-2)^2 + 25 where tt is seconds. What is the maximum height and when?

Example 18

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

Example 19

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

Example 20

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