University:
High School
Course:
High School Mathematics
Academic year:

2024
Views:

250

Pages:

4
Author:

Boston Gray

Solving Quadratic Equations Essential Question How can you use the graph of a quadratic equation to determine the number of real solutions of the equation? EXPLORATION: Matching a Quadratic Function with Its Graph Work with a partner. Match each quadratic function with its graph. Explain your reasoning. Determine the number of x-intercepts of the graph. 2. f(x) = x2 - 2x + I 5. f(x) = '.-x2 + 2x - 1 (\ :¾ 4 -6 -4 ){ 4 -6 D. -6 -4 ¼. 4 4 -6 -4 4 -6 -4 -4 ,!, 2x -4- _2 3. f(x) = x2 6. - - Notetaking with Vocabulary (continued) Zero-Product Property Words If the product of two expressions is zero, then one or both of the expressions equal zero. Algebra If A and B are expressions and AB Extra Practice .,---.}) n 2 = 0, then A = 0 or B = 0. the equation by graphing. r 1. x - 1 lx + 24 = 0 2. '2.._ - - In Exercises 4-6, solve the equation using square root/ V= - 2- 00 5. (2k + 3) 2 ---- - 19 = 81 z,, i, r;),,_ =iJ' o o -- -j - u Notetaking with Vocabulary In your own words, write the meaning of each vocabulary term. quadratic equation in one variable zero of a function Core Concepts Solving Quadratic Equations By graphing Find the x-intercepts of the related function y = ax2 + bx + c. Using square roots Write the equation in the form u 2 = d, where u is an algebraic expression, and solve by taking tb square root of each side. By factoring Write the polynomial equatjonfa;2 + bx + c-::_ OJin factored form and solve using theZero-Product Property. ------------------------- BII Notetaking with Vocabulary Date ____ (continued) In Exercises 7-9, solve the equation by factoring. a. x 2 = 14x - 40 '.. :::-o 10. Which equations have roots that are equiva ent to the x-intercepts of the gn A. - 2x 2 - 1 Ox - 8 = 0 c. (x - l)(x + 4) E. 6x2 0 e. x2 D. - 3x = 4 (x - 1)2 + 4 0 18x + 24 11. A skydiver drops out of an airplane that is flying at an altitude of 4624 feet. a.Use the formula h = -16t 2 + '1o to write an equation that gives the skydiver's height h (in feet) during free fall seconds after the skydiver drops out of the airplane. b.It is possible for the skydiver to wait 18 seconds before pulling the parachute cord? Explain.