Chapter 8 Warm up 8
Solve each equation by graphing the related function. Get out your graphing calculator and let's make sure we all understand how to graph these on the calculator and use the calculator to find the solution(s).
1. x2 + 2x = 8
2. 3x – 5 = x2
Chapter 8 Warm up 6 answers
Chapter 8.6 Warm up regular
Find each product.
2. (x – 11)(x + 5)
1. (x + 2)(x + 7)
3. (x – 10)2
Factor each polynomial.
4. x2 + 12x + 35
5. x2 + 2x – 63 6. x2 – 10x + 16
7. 2x2 – 16x + 32 Chapter 8.6 Warm up answers
8.6 Solving Quadratic Equations by Factoring
Learning Target
I can solve quadratic equations by factoring.
Who uses this?
In order to determine how many
seconds she will be in the air, a high
diver can use a quadratic equation.
8.6 Solving Quadratic Equations by Factoring
You have solved quadratic equations by graphing. Another method used to solve quadratic equations is to factor and use the Zero Product Property.
I. Solve using zero products property
1. (x – 7)(x + 2) = 0
2. (x + 4)(x – 3) = 0
x – 7 = 0 or x + 2 = 0
x = 7 or x = –2 The solutions are 7 and –2.
Notice these quadratics were already in factored form.
If a quadratic equation is written in standard form, ax2 + bx + c = 0, then to solve the equation, you may need to factor before using the Zero Product Property.
II. Solve by factoring
3. x2 – 6x + 8 = 0
4. x2 + 4x = 21
Check Graph the related quadratic function. The zeros of the related function should be the same as the solutions from factoring.
II. Solve by factoring
5. x2 – 12x + 36 = 0
6. –2x2 = 20x + 50
What should the graph look like? Let's check.
II. Solve by factoring
7. x2 – 6x + 9 = 0
Your turn..
8. x2 + 4x = 5
II. Solve by factoring
9. x2 + 4x = 5
11. 30x = –9x2 – 25
Your turn..
10. 30x = –9x2 – 25
12. 3x2 – 4x + 1 = 0
II. Application
The height in feet of a diver above the water can be modeled by h(t) = –16t2 + 8t + 8, where t is time in seconds after the diver jumps off a platform. Find the time it takes for the diver to reach the water.
Factor and solve...
II. Application
The equation for the height above the water for another diver can be modeled by h = –16t2 + 8t + 24. Find the time it takes this diver to reach the water. Factor and solve...
Assignment
8.6
Pages 565­567:
20­44 (even)
47­49
50 ­ 58 (even)
59­61