University:
High School
Course:
High School Algebra
Academic year:

2021
Views:

25

Pages:

2
Author:

treyjunak4

3.4 | Quadratic Formula Quadratic Equation ax² + bx + c = 0 a a a a a "get rid of 'a'" x² + (b/a)x + c/a = 0 x² + (b/a)x = -c/a "move away" x² + (b/a)x + (b/2a)² = -c/a + (b/2a)² Complete the Square Steps Factor (x + b/2a)² = b²/4a² - c/a √(x + b/2a)² = √(b² - 4ac)/4a² x + b/2a = ±√(b² - 4ac)/2a x = -b/2a ± √(b² - 4ac)/2a Quadratic Formula x = -b ± √(b² - 4ac)/2a Extra Practice In Exercises 1-3, solve the equation using the Quadratic Formula. Use a graphing calculator to check your solutions(s). x² - 7x - 18 = 0 x = (7 ± √(7² - 4(1)(-18)))/2 x = (7 ± √121)/2 x = (7 ± 11)/2 x = 9, -2 w² - 4w - 1 = 0 w = (4 ± √(4² - 4(1)(-1)))/2 w = (4 ± √20)/2 w = 2 ± √5 -7z = -4z² - 3 4z² - 7z + 3 = 0 z = (7 ± √(7² - 4(4)(3)))/8 z = (7 ± √1)/8 z = 1, 3/4 A baseball player hits a foul ball straight up in the air from a height of 4 feet off the ground with an initial velocity of 85 feet per second. a. Write a quadratic function that represents the height h of the ball t seconds after the ball is hit. h(t) = -16t² + 85t + 4 b. Will the ball hit 110 feet off the ground? Explain your reasoning. 110 = -16t² + 85t + 4 0 = -16t² + 85t - 106 Use the quadratic formula to solve for t. The discriminant (b² - 4ac) will be negative, meaning there are no real solutions. Therefore, the ball will not reach a height of 110 feet. c. The catcher catches the ball 6 feet from the ground. How long is the ball in the air? 6 = -16t² + 85t + 4 0 = -16t² + 85t - 2 Use the quadratic formula to solve for t.