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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 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?