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# Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities - PowerPoint PPT Presentation

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities. Chapter 5 – Quadratic Functions and Inequalities 5.2 – Solving Quadratic Equations by Graphing. 5.2 – Solving Quadratic Equations by Graphing. Quadratic equation – when a quadratic function is set to a value

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Presentation Transcript

Chapter 5 – Quadratic Functions and Inequalities

5.2 – Solving Quadratic Equations by Graphing

5.2 – Solving Quadratic Equations by Graphing Inequalities

• Quadratic equation– when a quadratic function is set to a value

• ax2 + bx + c = 0, where a ≠ 0

• Standard form – where a, b, and c are integers

5.2 – Solving Quadratic Equations by Graphing Inequalities

• Roots – solutions of a quadratic equation

• One method for finding roots is to find the zeros of the function

• Zeros – the x-intercepts of its graph

• They are solutions because f(x) = 0 at those points

5.2 – Solving Quadratic Equations by Graphing Inequalities

• Example 1

• Solve x2 – 3x – 4 = 0 by graphing.

5.2 – Solving Quadratic Equations by Graphing Inequalities

• A quadratic equation can have one real solution, two real solutions, or no real solution.

5.2 – Solving Quadratic Equations by Graphing Inequalities

• Example 2

• Solve x2 – 4x = -4 by graphing.

5.2 – Solving Quadratic Equations by Graphing Inequalities

• Example 3

• Find two real numbers with a sum of 4 and a product of 5, or show that no such numbers exist.

5.2 – Solving Quadratic Equations by Graphing Inequalities

• Often exact roots cannot be found by graphing

• We can estimate solutions by stating the integers between which the roots are located.

5.2 – Solving Quadratic Equations by Graphing Inequalities

• Example 4

• Solve x2 – 6x + 3 = 0 by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

5.2 – Solving Quadratic Equations by Graphing Inequalities

• Example 5

• The highest bridge in the U.S. is the Royal Gorge Bridge in Colorado. The deck is 1053 feet above the river. Suppose a marble is dropped over the railing from a height of 3 feet above the bridge deck. How long will it take the marble to reach the surface of the water, assuming there is no air resistance? Use the formula h(t) = -16t2 + h0, where t is time in seconds and h0 is the initial height above the water in feet.

5.2 – Solving Quadratic Equations by Graphing Inequalities

Example 5 (cont.)

The highest bridge in the U.S. is the Royal Gorge Bridge in Colorado. The deck is 1053 feet above the river. Suppose a marble is dropped over the railing from a height of 3 feet above the bridge deck. How long will it take the marble to reach the surface of the water, assuming there is no air resistance? Use the formula h(t) = -16t2 + h0, where t is time in seconds and h0 is the initial height above the water in feet.

5.2 – Solving Quadratic Equations by Graphing Inequalities

HOMEWORK

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#15 – 29 odd, 30 – 31, 44 – 45