1. Do Now 4/15/10 Take out HW from yesterday. Copy HW in your planner.
Practice worksheet 10.2 form B odds
Copy HW in your planner.
Text p. 647, #8, 14, 17, 24, 30
Quiz sections Monday.

2. Homework Practice 10.2 Form B odds
1) a = 6, b = 3, c = 5
3) a = 7, b = -3, c = -1
5) a = 3/4, b = 0, c = -10
7) up; x = 0; (0,-5)
9) down; x = 3/2; (3/2, 23/2)
11) up; x = -1; (-1, -5)
13) up; x = -5; (-5, -33/2)
15) down; x = 3/2; (3/2, -5/4)
17) down; x = 7/4; (7/4, 57/8)
19)
21)
23-31) on overhead
33) maximum; (1,3)
35) 12 ft x 3 4 5 6 7 y
-18
-21
-22 x -1 1 2 3 y
17/2 7
13/2

3. Objective
SWBAT solve quadratic equations by graphing

4. Section 10.3 “Solve Quadratic Equations by Graphing”
an equation that is in the standard form ax² + bx + c = 0, where a = 0.
Solve by Factoring (Chapter 9)
Solve by Graphing y
x² - 6x + 5 = 0
x² - 6x + 5 = 0 x
(x – 1)(x – 5) = 0
x = 1 or x = 5
To solve this equation graph y = x² - 6x From the graph you can see that the intercepts are 1 and 5.
(Remember This???)

5. Solving Quadratic Equations by Graphing
To solve a quadratic equation by graphing, first write the equation in standard form, ax² + bx + c = 0. Then graph the equation. The x-intercepts of the graph are the solutions, or roots, of the equation.
Quadratic equations can have one of three types of solutions:
Two solutions
(2) One solution
(3) No solution y y y x x x
One x-intercept
No x-intercepts
Two x-intercepts

6. Solve a quadratic equation having two solutions
EXAMPLE 1
Solve a quadratic equation having two solutions
Solve x2 – 2x = 3 by graphing.
SOLUTION
STEP 1
Write the equation in standard form.
x2 – 2x = 3
Write original equation.
x2 – 2x – 3 = 0
Subtract 3 from each side.
STEP 2
Graph the function y = x2 – 2x – 3.
The x-intercepts are – 1 and 3

7. Solve a quadratic equation having two solutions
EXAMPLE 1
Solve a quadratic equation having two solutions
ANSWER
The solutions of the equation x2 – 2x = 3 are – 1 and 3.
CHECK:
You can check – 1 and 3 in the original equation.
x2 – 2x = 3
x2 – 2x = 3
Write original equation.
(–1)2 –2(–1) 3 = ?
(3)2 –2(3) 3 = ?
Substitute for x.
3 = 3
3 = 3
Simplify. Each solution checks.

8. Solve a quadratic equation having one solution
EXAMPLE 2
Solve a quadratic equation having one solution
Solve – x2 + 2x = 1 by graphing.
SOLUTION
STEP 1
Write the equation in standard form.
– x2 + 2x = 1
Write original equation.
– x2 + 2x – 1 = 0
Subtract 1 from each side.
STEP 2
Graph the function y = – x2 + 2x – 1.
The x-intercept is 1.

9. Solve a quadratic equation having no solution
EXAMPLE 3
Solve a quadratic equation having no solution
Solve x2 + 7 = 4x by graphing.
SOLUTION
STEP 1
Write the equation in standard form.
x = 4x
Write original equation.
x2 – 4x + 7 = 0
Subtract 4x from each side.
STEP 2
Graph the function y = x2 – 4x + 7.
The equation x² + 7 = 4x has no solution because there is no x-intercept.

10. EXAMPLE 4
Find the zeros of a quadratic function
Find the zeros of f(x) = x2 + 6x – 7.
SOLUTION
Graph the function f(x) = x x –7.
The x-intercepts are – 7 and 1.
ANSWER
The zeros of the function are – 7 and 1.
CHECK
Substitute – 7 and 1 in the original function.
f(– 7) = (– 7)2 + 6(– 7) – 7 = 0
f(1) = (1)2 + 6(1) – 7 = 0

11. Homework
Text p. 647, #8, 14, 17, 24, 30