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:
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:
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