Practice Zeros of a Quadratic in Math

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

Quick Recap

The zeros (or roots) of a quadratic function f(x) = ax^2 + 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.

Example 1

easy
Find the zeros of f(x) = x^2 - 7x + 10.

Example 2

medium
Find the zeros of g(x) = 2x^2 - 8x.

Example 3

easy
Find the zeros of h(x) = x^2 - 1.

Example 4

hard
How many zeros does f(x) = x^2 + 4 have over the reals?