1. Section 4.5 – Quadratic Equations
Students will be able to:
Create equations and inequalities in one variable and use them to solve problems
Identify zeros of polynomials when suitable factorizations are available
Lesson Vocabulary:
Zero of a Function
Zero Product Property

2. Section 4.5 – Quadratic Equations

3. Section 4.5 – Quadratic Equations
Wherever the graph of the function f(x) intersects the x-axis, f(x) = 0.
A value of x for which f(x) = 0 is a zero of the function.

4. Section 4.5 – Quadratic Equations
Essential Understanding:
To find the zeros of a quadratic function
y = ax2 + bx + c, solve the related quadratic equation
0 = ax2 + bx + c.
You can solve some quadratic equations in standard form by factoring the quadratic expression and using the Zero-Product Property.

5. Section 4.5 – Quadratic Equations
Problem 1:
What are the solutions of the quadratic equation
x2 – 5x + 6 = 0

6. Section 4.5 – Quadratic Equations
Problem 1:
What are the solutions of the quadratic equation
x2 – 7x = -12

7. Section 4.5 – Quadratic Equations
Problem 1:
What are the solutions of the quadratic equation
2x2 + 6x = -4

8. Section 4.5 – Quadratic Equations
Problem 1:
What are the solutions of the quadratic equation
2x2 = 8x

9. Section 4.5 – Quadratic Equations
Problem 1:
What are the solutions of the quadratic equation
3x2 = 16x + 12

10. Section 4.5 – Quadratic Equations
Problem 2:
What are the solutions of the quadratic equation
5x2 + 30x + 14 = 2 – 2x

11. Section 4.5 – Quadratic Equations
Problem 2:
What are the solutions of the quadratic equation
4x2 – 14x + 7 = 4 – x

12. Section 4.5 – Quadratic Equations
Problem 3:
What are the solutions of the quadratic equation
2x2 + 7x = 15

13. Section 4.5 – Quadratic Equations
Problem 3:
What are the solutions of the quadratic equation
x2 + 2x – 24 = 0

14. Section 4.5 – Quadratic Equations
Problem 3:
What are the solutions of the quadratic equation
6x2 = -19x – 15

15. Section 4.5 – Quadratic Equations
Problem 4:
How far did the frog jump?
How high did the frog jump?
What is a reasonable domain for such a frog jumping function?

16. Section 4.5 – Quadratic Equations
Problem 5:
Suppose you have an outdoor pool measuring 25 feet by 10 feet. You want to add a cement walkway around the pool. If the walkway will be 1 ft thick and you have 304 cubic feet of cement, how wide should the walkway be?

17. Section 4.5 – Quadratic Equations
Problem 6:

18. Section 4.5 – Quadratic Equations