Quadratic Formula Worksheet

This quadratic formula worksheet gives students practice identifying coefficients, substituting carefully, and simplifying answers correctly. The printable set includes 12 randomized questions and an answer key on page 2.

What is the Quadratic Formula?

The quadratic formula is a method for solving any quadratic equation written in the form $ax^2 + bx + c = 0$. It is especially useful when a quadratic is hard to factor.

How to Use the Quadratic Formula

1. Rewrite the equation in standard form: $ax^2 + bx + c = 0$.
2. Identify the values of $a$, $b$, and $c$.
3. Substitute into the quadratic formula.
4. Simplify carefully to find the solution or solutions.

Example

Solve $x^2 - 4x - 5 = 0$

Here, $a = 1$, $b = -4$, and $c = -5$.

Substitute into the formula:

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-5)}}{2(1)}$

$x = \frac{4 \pm \sqrt{16 + 20}}{2} = \frac{4 \pm 6}{2}$

So the solutions are $x = 5$ and $x = -1$.

FAQ

Q: Can the quadratic formula solve every quadratic equation?
A: Yes. As long as the equation is quadratic and written in standard form, the quadratic formula can be used.

Q: What does the discriminant tell me?
A: The discriminant, $b^2 - 4ac$, tells you whether the equation has two real solutions, one real solution, or no real solutions.