1. Warm-up August 16, 2016
If the solutions to a quadratic equation are 2 and -3, what is the quadratic equation?
Find the solution to the quadratic equation,

2. Unit 1: Quadratic Functions Review
August 15, 2017
Unit 1: Quadratic Functions
Review
Daily Agenda
Warm-up
Imaginary Numbers – Review
Solve Quadratic Equations using Square Roots
Solve Quadratic Equations by Factoring
Solve Quadratics using Quadratic Formula
Direct Explanation
Guided Practice – HW review
Students will practice solving quadratic equations using various methods
Independent practice #1 and #2
Worktime
Address misconceptions
Exit Slip – Error Analysis
Closing

3. HW Review 8/15/2016

4. If a and b are real numbers and if , then or .
11.6 – Solving Quadratic Equations by Factoring
Zero Factor Property:
If a and b are real numbers and if ,
then or
Examples:

5. Solving Quadratic Equations: 1) Write the equation in standard form.
11.6 – Solving Quadratic Equations by Factoring
Solving Quadratic Equations:
1) Write the equation in standard form.
2) Factor the equation completely.
3) Set each factor equal to 0.
4) Solve each equation.
5) Check the solutions (in original equation).

6. 11.6 – Solving Quadratic Equations by Factoring

7. 11.6 – Solving Quadratic Equations by Factoring
If the Zero Factor Property is not used, then the solutions will be incorrect

8. 11.6 – Solving Quadratic Equations by Factoring

9. 11.6 – Solving Quadratic Equations by Factoring

10. 11.6 – Solving Quadratic Equations by Factoring

11. 11.6 – Solving Quadratic Equations by Factoring

12. 11.6 – Solving Quadratic Equations by Factoring

13. Quadratic Equations Complete practice #1 – 19 odd
Quadratic Equations Matching Game
HW: complete practice #2 – 20 even

14. 11.7 – Quadratic Equations and Problem Solving
A cliff diver is 64 feet above the surface of the water. The formula for calculating the height (h) of the diver after t seconds is:
How long does it take for the diver to hit the surface of the water?
seconds

15. 11.7 – Quadratic Equations and Problem Solving
The square of a number minus twice the number is 63. Find the number.
x is the number.

16. 11.7 – Quadratic Equations and Problem Solving
The length of a rectangular garden is 5 feet more than its width. The area of the garden is 176 square feet. What are the length and the width of the garden?
The width is w.
The length is w+5.
feet
feet

17. 11.7 – Quadratic Equations and Problem Solving
Find two consecutive odd numbers whose product is 23 more than their sum?
Consecutive odd numbers:

18. 11.7 – Quadratic Equations and Problem Solving
The length of one leg of a right triangle is 7 meters less than the length of the other leg. The length of the hypotenuse is 13 meters. What are the lengths of the legs?
meters
meters

19. Solving Quadratic Equations by the Quadratic Formula

20. THE QUADRATIC FORMULA
When you solve using completing the square on the general formula you get:
This is the quadratic formula!
Just identify a, b, and c then substitute into the formula.

21. WHY USE THE QUADRATIC FORMULA?
The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it.
An important piece of the quadratic formula is what’s under the radical:
b2 – 4ac
This piece is called the discriminant.

22. WHY IS THE DISCRIMINANT IMPORTANT?
The discriminant tells you the number and types of answers
(roots) you will get. The discriminant can be +, –, or 0
which actually tells you a lot! Since the discriminant is
under a radical, think about what it means if you have a
positive or negative number or 0 under the radical.

23. WHAT THE DISCRIMINANT TELLS YOU!
Value of the Discriminant
Nature of the Solutions
Negative
2 imaginary solutions
Zero
1 Real Solution
Positive – perfect square
2 Reals- Rational
Positive – non-perfect square
2 Reals- Irrational

24. Example #1 a=2, b=7, c=-11 Discriminant = Discriminant =
Find the value of the discriminant and describe the nature of the roots (real,imaginary, rational, irrational) of each quadratic equation. Then solve the equation using the quadratic formula) 1.
a=2, b=7, c=-11
Discriminant =
Value of discriminant=137
Positive-NON perfect square
Nature of the Roots – 2 Reals - Irrational
Discriminant =

25. Example #1- continued
Solve using the Quadratic Formula

26. Solving Quadratic Equations by the Quadratic Formula
Try the following examples. Do your work on your paper and then check your answers.