Quadratic Formula Practice Worksheet
Practice solving quadratic equations using the quadratic formula with step-by-step solutions.
Use the quadratic formula to solve each equation. Simplify your answers whenever possible.
Quadratic Formula
\[
x=
\frac{
-b \pm \sqrt{b^2-4ac}
}{
2a
}
\]
Level 1: Basic Quadratics
Problem 1
\[
x^2 + 5x + 6 = 0
\]
Show solution
\(a=1,\ b=5,\ c=6\)
\[
x=
\frac{
-5 \pm \sqrt{25-24}
}{
2
}
\]
\[
x=-2,\ -3
\]
Problem 2
\[
x^2 - 7x + 10 = 0
\]
Show solution
\(a=1,\ b=-7,\ c=10\)
\[
x=
\frac{
7 \pm \sqrt{49-40}
}{
2
}
\]
\[
x=5,\ 2
\]
Problem 3
\[
x^2 + 4x - 12 = 0
\]
Show solution
\(a=1,\ b=4,\ c=-12\)
\[
x=
\frac{
-4 \pm \sqrt{16+48}
}{
2
}
\]
\[
x=
\frac{
-4 \pm 8
}{
2
}
\]
\[
x=2,\ -6
\]
Problem 4
\[
2x^2 + 3x - 2 = 0
\]
Show solution
\(a=2,\ b=3,\ c=-2\)
\[
x=
\frac{
-3 \pm \sqrt{9+16}
}{
4
}
\]
\[
x=
\frac{
-3 \pm 5
}{
4
}
\]
\[
x=\frac{1}{2},\ -2
\]