Practice Zeros of a Quadratic in Math

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

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Quick Recap

The zeros (or roots) of a quadratic function f(x)=ax2+bx+c are the values of x where f(x)=0. Graphically, they are the x-intercepts of the parabola.

The zeros are where the parabola crosses or touches the x-axis. A parabola can cross twice (two zeros), just touch once (one repeated zero), or miss entirely (no real zeros). You can find them by factoring, completing the square, or using the quadratic formula.

Showing a random 20 of 50 problems.

Example 1

hard
Find the zeros of f(x)=x2+4x+1 by completing the square.

Example 2

easy
How many real zeros does f(x)=(x−5)2 have?

Example 3

medium
Find the zeros of f(x)=−x2+5x+6.

Example 4

challenge
A quadratic f(x)=x2+bx+c has zeros 2 and −5. Find b and c.

Example 5

easy
Find the zeros of f(x)=x2−100.

Example 6

hard
If a quadratic with leading coefficient 1 has zeros −1 and 4, write it in standard form.

Example 7

challenge
If f(x)=x2+px+q has zeros r and s with r+s=5 and r2+s2=13, find p and q.

Example 8

medium
Find the sum and product of the zeros of f(x)=2x2+5x−3.

Example 9

easy
How many real zeros does f(x)=x2+25 have?

Example 10

easy
Find the zeros of h(x)=x2−1.

Example 11

easy
Find the zeros of f(x)=x2−5x+6.

Example 12

easy
Find the zeros of f(x)=x2−7x+10.

Example 13

easy
Find the zeros of f(x)=(x−3)(x+8).

Example 14

easy
Is f(0) a zero of f(x)=x2−4?

Example 15

medium
If −4 is a zero of f(x)=x2+bx+4, find b.

Example 16

medium
If 3 is a zero of f(x)=x2+bx−12, find b.

Example 17

medium
Find the zeros of f(x)=2x2+5x+2.

Example 18

medium
Find the zeros of f(x)=3x2−7x+2.

Example 19

medium
Find the zeros of f(x)=x2−2x−8 by factoring.

Example 20

medium
Find the zeros of f(x)=x2+6x+5 by factoring.
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