1. Drill #92
Identify the maximum or minimum value of each quadratic function, then state the domain and range of each.

2. Drill #93
Identify the a.) max/min the b.) domain and range, and c.) roots (if any) of each graph:
Vert: (3/2, -1/5) Vert: (1, 0) Vert: (0, -1)

3. Drill #94
Identify the a.) max/min the b.) domain and range, and c.) roots (if any) of each graph:
Vert: (0, -1) Vert: (-2, 0) Vert: (2, 2)

4. Drill #95
Write a quadratic equation in standard form with the given root(s).
1. { -1, 6}
2. { ¾ , -½ }
3. { 3 }

5. 6-2 Solving Quadratic Equations
Objective: To estimate solutions to quadratic equations by graphing and to find the zeros of quadratic equations using the zero-product property.

6. (1.) zeros
Definition: The x- coordinates where a function crosses the x- axis (the x- intercepts). These are all the values such that f(x) = 0.
(2.) roots: The zeros of a function are also called roots of the function. They are values of x that satisfy

7. Solving a Quadratic Equation by Graphing*
1. Find the vertex (x = -b/2a)
2. Find 2 points on either side of the vertex.
3. Draw the parabola
4. Identify the points where the parabola crosses the x-axis. (if it is between two numbers, estimate the value)
NOTE: If the parabola does not cross the x-axis then it has no zeroes (or roots)

8. Examples*
Find the Zeros: Two solutions
Ex1. Ex2.

9. Examples*
Find the Zeros
Ex3. Ex4.

10. Graphing on the TI-83/84 To enter the function:
1. Enter the equation into [y1 =]
2. To view graph [graph]
3. To adjust axes [window]
Equation must be in

11. Study Guide Examples*
Find the roots of each quadratic by graphing…

12. Writing Equations In Standard Form*
If a quadratic equation has roots
to write the equations in standard form:
1. Set up the equation
2. FOIL (Multiply)
3. Simplify (combine like terms)
Example: SG 1, #1

13. Writing Equations in Standard Form (w/ Fractional Roots)
If a quadratic has fractional roots…
Before you FOIL
1. Find a common denominator for each factor
2. Multiply each side by the product of the denominators (cancel the denominators)
Example: SG 2, #14

14. Writing Equations in Standard Form (w/ One Root)
If a quadratic has one root…
1. Then the root is repeated…
use the same root for x1 and x2
Example: Root = 6

15. Sketch a Graph*
Sketch a graph of a quadratic with the following properties:
Ex1: roots = {1, 4}; a > 0
Ex2: roots = {1, 4}; a < 0
Ex3: roots = { 2 }; a > 0
Ex4: roots = { }; a < 0

16. (3.) Zero Product Property**
Definition: If the product of two numbers a(b) = 0 then
either a = 0 or b = 0 or both
Example:
x (x – 1) = 0
x = 0 or x – 1 = 0
x = 1

17. Solving Quadratic Equations by Factoring*
To solve a quadratic equation by factoring:
1. Group all the terms onto the same side of the equation ( )
2. Factor the quadratic
3. Use the zero product property

18. Factoring Quadratic Equations
Examples: Skills Practice: 7, 9, 11
Classwork 8, 10, 12

19. Solving Quadratic Equations*
Examples:
No Linear Term:
No Constant:
Quadratic Coefficient (a) = 1:
Quadratic Coefficient (a) = 1