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Quadratics

Learn to solve quadratic equations and understand their graphs.

What You'll Learn:

  • Factoring
  • Identify the vertex (h, k)
  • Using the quadratic formula
  • Understand the parabola

Lesson 1:

Factoring

Lesson 1:

Factoring

Step 1:

Write in standard form and set equal to zero.

x²+5x+6=0

Step 2:

Find two numbers that multiply to 6 and add to 5. That’s 2 and 3.

(x+2)(x+3)=0

Step 3:

Set each factor equal to zero and solve.

x+2=0→x=−2

x+3=0→x=−3

Result

x=−2

and

x=−3

Lesson 2:

Quadratic Formula

Plug into the formula and solve.

Step 1:

Identify a, b, c.

x²+4x−5=0

a=1,b=4,c=−5

Step 2:

Plug into the formula.

x = - 4 ± 16 + 20 2
x = - 4 ± 36 2
x = (- 4 +/- 6) / 2

Step 3:

Solve both cases.

Result

x=1

and

x=−5

Practice Problems

Easy

x²+7x+12=0

x²−5x+6=0

Medium

x²+3x−5=0

2x²−x−3=0

Challenge

Find the vertex and x-intercepts of:

y=x²−4x+3

Sketch the parabola.

Common Mistakes to Avoid:

  • Not setting the equation equal to zero before factoring
  • Dropping the negative sign on b in the formula (−b, not b)
  • Forgetting the ± — there are usually TWO solutions

Quick Recap:

Quadratic Formula
Quadratic formula: x = - b ± b2 − 4ac 2a
Factored form: (x + a) (x + b) = 0 → x = −a, −b
Vertex x-value: x = - b 2a
Full vertex: plug x back in to get (x, y)
Answer Key:
Easy: (x = −3, −4), (x = 2, 3)
Medium: (x ≈ 1.19, −4.19), (x = 3/2, −1)
Challenge: Vertex: (2, −1) , x-intercepts: (1,0), (3,0)

Next:

Word Problems
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