# 4.5 Quadratic Equations Wherever the graph of a 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.

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4.5 Quadratic Equations Wherever the graph of a 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. To find the zeros of a quadratic function y = ax 2 + bx + c, solve the related quadratic equation 0 = ax 2 + bx + c.

Zero-Product Property You can solve some quadratic equations in standard form by factoring the quadratic expression and using the Zero-Product Property. Zero-Product Property: If ab = 0, then a = 0 or b = 0.

Solving a Quadratic Equation by Factoring What are the solutions of the quadratic equation x 2 – 5x + 6 = 0? Factor the quadratic expression. (x – 2)(x – 3) = 0 Use the Zero-Product Property. x – 2 = 0 or x – 3 = 0 x = 2 or x = 3 The solutions are x = 2 and x = 3.

Solving a Quadratic Equation with Tables What are the solutions of the quadratic equation 5x 2 + 30x + 14 = 2 – 2x? 5x 2 + 30x + 14 = 2 – 2x 5x 2 + 32x + 12 = 0 Use your calculator’s table feature to find the zeros.

Solving a Quadratic Equation with Tables Notice that when x = -6, y = 0. So, x = -6 is one zero. The second zero is between x = -1 and x = 0 – notice the change in sign for y – values. Change the x-interval to.1. The second zero is x = -0.4. The solutions are x = -6 and x = -0.4.

Solving a Quadratic Equation by Graphing What are the solutions of the quadratic equation 2x 2 + 7x = 15? 2x 2 + 7x = 15 2x 2 + 7x – 15 = 0 Use your calculator’s zero option in CALC feature to find the zeros. The solutions are x = -5 and x = 1.5.

More Practice!!!!! Homework – Textbook p. 229 #10 – 36 even.

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