Section 4.5 – Quadratic Equations

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Presentation transcript:

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 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.

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.

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

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

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

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

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

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

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

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

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

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

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?

Section 4.5 – Quadratic Equations Problem 6:

Section 4.5 – Quadratic Equations