Chapter 4: Quadratic Functions and Equations Section 4.7: The Quadratic Formula

Section 4.7: The Quadratic Formula Goal: To solve quadratic equations using the Quadratic Formula and to determine the number of solutions by using the discriminant

Section 4.7: The Quadratic Formula In this chapter, you have learned how to solve quadratic equations by factoring, isolating the variable, and completing the square While completing the square will always work to solve a quadratic, it can be a “messy” process if there are fractions involved Using the Quadratic Formula also always works for solving quadratics and may not involve “messy” fractions

Section 4.7: The Quadratic Formula The Quadratic Formula: the equation must be in standard form before using the quadratic formula If ax2 + bx + c = 0, then

Section 4.7: The Quadratic Formula Examples: 1. Use the quadratic formula to solve: 5x2 – 2x = 2

Section 4.7: The Quadratic Formula You try: 2. Solve x2 – 8x = 33 by using the Quadratic Formula

Section 4.7: The Quadratic Formula You try: 3. Solve x2 – 34x +289 = 0 by using the Quadratic Formula.

Section 4.7: The Quadratic Formula Application: 4. You sell wrapping paper as a charity fundraiser. The equation p = -6x2 + 280x – 1200 models the total profit p as a function of the price x per roll of paper. What is the smallest amount in dollars you can charge per roll of wrapping paper to make a profit of $1500?

Section 4.7: The Quadratic Formula The Discriminant: b2 – 4ac (the stuff under the square root in the quadratic equation) By evaluating the discriminant, the number or solutions and the type of solutions can be determined

Section 4.7: The Quadratic Formula The Discriminant and the Solutions

Section 4.7: The Quadratic Formula Examples: 5. What is the number of real solutions of –x2 + 14x = 49 ?

Section 4.7: The Quadratic Formula You try: 6. Find the value of the discriminant for each quadratic equation. Describe the number and type of roots for the equation. A) x2 + 3x + 5 = 0 B) x2 – 11x + 10 = 0

Section 4.7: The Quadratic Formula Application: 7. A rocket is launched from the ground with an initial vertical velocity of 150 ft/s. The function h = -16t2 + 150t models the height in feet of the rocket at time t in seconds. Will the rocket reach a height of 300 ft? Explain your answer.

Section 4.7: The Quadratic Formula Homework: Pg. 245 #12-38 (even)