Practice Quadratic Factored Form in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The factored form of a quadratic function is f(x)=a(x−r1)(x−r2), where r1 and r2 are the zeros (roots) of the function and a is the leading coefficient.

Each factor (x−r) equals zero when x=r. So the factored form literally shows you where the parabola crosses the x-axis—plug in either root and the whole expression becomes zero.

Showing a random 20 of 50 problems.

Example 1

easy
Find the roots of (x−2)(x−5)=0.

Example 2

medium
Factor 3x2−10x+8.

Example 3

easy
Factor x2−7x+12.

Example 4

medium
Find the vertex of f(x)=(x−2)(x−10).

Example 5

easy
Write a quadratic in factored form (leading coefficient 1) with zeros −6 and 1.

Example 6

easy
What are the zeros of f(x)=(x−1)(x+4)?

Example 7

medium
Factor completely: 2x2−18.

Example 8

medium
Factor 2x2+7x+3.

Example 9

easy
Find the zeros of h(x)=−3(x+2)(x−5).

Example 10

medium
Factor x2−11x+24.

Example 11

medium
Write the factored form of a parabola with roots −2 and 5 passing through (0,−20).

Example 12

medium
Find the axis of symmetry of f(x)=(x−1)(x−7).

Example 13

easy
Factor x2−9x+20.

Example 14

medium
Solve x2+6x=−8 by factoring.

Example 15

medium
Solve x2−7x+12=0 by factoring.

Example 16

medium
Write the factored form of the quadratic with roots −3 and 4 passing through (0,−24).

Example 17

challenge
For what values of k does x2+8x+k factor as (x+r)2 for some real r?

Example 18

easy
Factor x2+5x+6.

Example 19

hard
Find all k so x2+kx+18=0 has integer solutions.

Example 20

easy
Factor the difference of squares x2−16.
← Back to Quadratic Factored Form Worked Examples Formula Explained