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

Section 4.5 – Quadratic Equations

Section 4.5 – Quadratic EquationsWherever 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.

Section 4.5 – Quadratic EquationsEssential 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.

Section 4.5 – Quadratic EquationsProblem 1:

What are the solutions of the quadratic equation

x2 – 5x + 6 = 0

Section 4.5 – Quadratic EquationsProblem 1:

What are the solutions of the quadratic equation

x2 – 7x = -12

Section 4.5 – Quadratic EquationsProblem 1:

What are the solutions of the quadratic equation

2x2 + 6x = -4

Section 4.5 – Quadratic EquationsProblem 1:

What are the solutions of the quadratic equation

2x2 = 8x

Section 4.5 – Quadratic EquationsProblem 1:

What are the solutions of the quadratic equation

3x2 = 16x + 12

Section 4.5 – Quadratic EquationsProblem 2:

What are the solutions of the quadratic equation

5x2 + 30x + 14 = 2 – 2x

Section 4.5 – Quadratic EquationsProblem 2:

What are the solutions of the quadratic equation

4x2 – 14x + 7 = 4 – x

Section 4.5 – Quadratic EquationsProblem 3:

What are the solutions of the quadratic equation

2x2 + 7x = 15

Section 4.5 – Quadratic EquationsProblem 3:

What are the solutions of the quadratic equation

x2 + 2x – 24 = 0

Section 4.5 – Quadratic EquationsProblem 3:

What are the solutions of the quadratic equation

6x2 = -19x – 15

Section 4.5 – Quadratic EquationsProblem 4:

How far did the frog jump?

How high did the frog jump?

What is a reasonable domain for such a frog jumping function?

Section 4.5 – Quadratic EquationsProblem 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?

Section 4.5 – Quadratic EquationsProblem 6:

Section 4.5 – Quadratic Equations