Virginia SOL Math / Algebra I / Equations & Inequalities

A.EI.3

Solving Quadratic Equations

What you'll learn

  • Solve quadratic equations by factoring
  • Solve quadratic equations using square roots
  • Apply the quadratic formula

Words to know

Quadratic equation —
an equation of the form ax^2 + bx + c = 0
Root —
a value of x that makes the equation equal zero
Zero product property —
if a*b = 0 then a = 0 or b = 0
Quadratic formula —
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
Discriminant —
the value b^2 - 4ac under the radical
Parabola —
the U-shaped graph of a quadratic

Why it matters Quadratics model paths of thrown objects and areas, and their roots tell us key moments like when a ball hits the ground.

Worked examples

Model ItI do

Solve x^2 - x - 6 = 0 by factoring.

Factor: (x - 3)(x + 2) = 0. By the zero product property, x = 3 or x = -2, which are the graph's x-intercepts.

Try It TogetherWe do

Solve x^2 = 49 using square roots.

Take the square root of both sides, keeping both signs: x = +/- 7. So x = 7 or x = -7.

Now YouYou do

Solve x^2 + 5x + 6 = 0 by factoring.

Find two numbers that multiply to 6 and add to 5, then set each factor to zero. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Solve: (x - 5)(x + 2) = 0.

  2. 2.Solve: x^2 = 36.

  3. 3.Solve: x^2 - 4 = 0.

On Level

The core Quick Check from the book.

  1. 1.Solve: (x - 4)(x + 1) = 0.

  2. 2.Solve: x^2 = 25.

  3. 3.Factor and solve: x^2 - 9 = 0.

  4. 4.In ax^2 + bx + c = 0, name the value b^2 - 4ac.

  5. 5.Solve: x^2 - 7x + 10 = 0.

Challenge

Stretch your thinking.

  1. 1.Solve: x^2 + 2x - 8 = 0 by factoring.

  2. 2.Find the discriminant of x^2 + 3x + 2 = 0.

  3. 3.Solve using the quadratic formula: x^2 - 4x + 3 = 0.