Practice Quadratic Functions 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 function is a polynomial function of degree 2, written as $f(x) = ax^2 + bx + c$ with $a \neq 0$ , whose graph is a U-shaped curve called a parabola that opens upward when $a > 0$ or downward when $a < 0$ .

The path of a thrown ball — rising then falling — traces a parabola opening downward.

Showing a random 20 of 50 problems.

Example 1

easy

Evaluate

f(x) = x^2 + 1

x = 3

Example 2

medium

Find the zeros of

f(x) = x^2 - 5x + 6

by factoring.

Example 3

easy

What is the constant term

c

f(x) = 2x^2 - 5x + 7

Example 4

medium

Find the minimum value of

f(x) = x^2 - 4x + 7

Example 5

challenge

Solve

2x^2 - 3x - 2 = 0

with the quadratic formula.

Example 6

easy

Find the axis of symmetry of

f(x) = x^2 - 8x + 5

Example 7

medium

A quadratic has zeros at

x = -2

and

x = 5

and passes through

(0, -20)

. Find

f(x)

Example 8

medium

What is the range of

f(x) = 2x^2 - 8x + 5

Example 9

hard

Find the equation of the parabola with

x

-intercepts

-3

and

1

and passing through

(2, 10)

Example 10

easy

f(x) = ax^2 + bx + c

, why must

a \ne 0

Example 11

medium

Does the parabola

g(x) = -2x^2 + 4x + 1

open upward or downward? Find its maximum value.

Example 12

medium

Write

f(x) = x^2 - 9

in factored form.

Example 13

hard

f(x) = ax^2 + bx + c

has vertex

(1, 4)

and

f(3) = 0

, find

a

b

c

Example 14

hard

Find the equation of the tangent line to

y = x^2

at the point

(3, 9)

using only quadratic properties (without calculus).

Example 15

challenge

f(x) = x^2 + px + q

and

f(x) \geq 0

for all real

x

, what is the relation between

p

and

q

Example 16

medium

Convert

y = (x - 3)^2 + 2

to identify the vertex.

Example 17

medium

Find the vertex and axis of symmetry of

f(x) = 2x^2 - 8x + 3

Example 18

easy

How many

x

-intercepts can a parabola have at most?

Example 19

easy

Identify the domain of any quadratic function

f(x) = ax^2 + bx + c

Example 20

easy

Find

f(-2)

for

f(x) = x^2 - 3x + 1

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Related Concepts

Linear Functions Exponents Quadratic Formula Polynomials