Download Section 3.1 Solving by Graphing

• A quadratic equation in one variable is an
equation that can be written in the standard
form 𝑎𝑥 2 + 𝑏𝑥 + 𝑥 = 0, where 𝑎, 𝑏, 𝑎𝑛𝑑 𝑐 are
real numbers and 𝑎 ≠ 0.
• A root of an equation is a solution of the
equation.
WAYS TO SOLVE QUADRATIC EQUATIONS
1. SOLVING BY GRAPHING
2. SOLVING USING SQUARE ROOTS
3. SOLVING BY FACTORING (AKA ZERO-PRODUCT
PROPERTY)
WHEN SOLVING BY GRAPHING:
1. PUT THE EQUATION INTO STANDARD FORM: 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
2
2. GRAPH THE RELATED FUNCTION: 𝑦 = 𝑎𝑥 + 𝑏𝑥 + 𝑐
3. THE SOLUTIONS TO THE EQUATION WILL BE THE X-INTERCEPTS
(AKA ROOTS)
SOLVE 𝑥 + 2𝑥 = 3 BY GRAPHING
2
•STEP 1: GET THE EQUATION INTO STANDARD FORM
𝑥 2 + 2𝑥 − 3 = 0
•STEP 2: DETERMINE THE RELATED FUNCTION
𝑦 = 𝑥 2 + 2𝑥 − 3
•STEP 3: FIND THE VERTEX
−1, −4
•STEP 4: MAKE A TABLE OF VALUES
x
y
−𝟑
−𝟐
−𝟏
−4
0
1
CONTINUED
•STEP 5: GRAPH
•STEP 6: WRITE THE SOLUTIONS
𝑥 = −3 AND 𝑥 = 1
SOLVE 𝑥 + 8 = 6𝑥 BY GRAPHING
2
Standard Form:
Related Function:
x
y
Solutions:
SOLVE 𝑥 = −7𝑥 − 10 BY GRAPHING
2
Standard Form:
Related Function:
x
y
Solutions:
SOLVE 𝑥 − 8𝑥 = −16 BY GRAPHING
2
Standard Form:
Related Function:
x
y
Solutions:
SOLVE −𝑥 = 2𝑥 + 4 BY GRAPHING
2
Standard Form:
Related Function:
x
y
Solutions:
HOMEWORK
•10.3 HOMEWORK WORKSHEET (ALL PROBLEMS)