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

2022
Views:

111

Pages:

2
Author:

hanzestisswj

A wading pool problem: Given: depth = 1 foot, volume = 108 cubic feet, width (w) = length (l) - 12 feet Asked: (a) Write an equation for the volume of the pool. (b) Find the dimensions of the pool by completing the square. Completing the Square: Several quadratic equations are given, and students are asked to complete the square to rewrite them in vertex form or standard form. Examples: x² + 2x = 17 x² + 4x + 6 = 10 x² - 14x + 2 = 12 Circle Equations: Students are asked to put equations of circles into standard form (x - h)² + (y - k)² = r² and identify the center (h, k) and radius (r). Examples: x² + y² = 4 x² + y² + 6x = 40 x² + y² - 2x + 4y = 76 Problem 16: A wading pool is 1 foot deep and has a volume of 108 cubic feet. The width is 12 feet less than the length. a. Write an equation that represents the volume of the wading pool. b. Find the dimensions of the wading pool by completing the square. Solution to Problem 16: V = d * w * L 108 = (1) * (L - 12) * L 108 = L^2 - 12L 144 = L^2 - 12L + 36 12^2 = (L - 6)^2 12 = L - 6 L = 18 feet W = 6 feet Problem 17: Put the equation into Vertex form. x^2 + 2x = 17 x^2 + 2x + 1 = 17 + 1 (x + 1)^2 = 18 (x + 1)^2 - 18 = 0 Problem 18: x^2 + 4x + 6 = 10 x^2 + 4x + 4 = 4 + 4 (x + 2)^2 = 8 (x + 2)^2 - 8 = 0 Problem 19: x^2 - 14x + 2 = 12 x^2 - 14x + 49 = 10 + 49 (x - 7)^2 = 59 (x - 7)^2 - 59 = 0 Problem 20: Put the equation into standard Circle form. Indicate what the center and radius is. x^2 + y^2 = 4 Center = (0, 0) Radius = 2 Problem 21: x^2 + y^2 + 6x = 40 x^2 + 6x + 9 + y^2 = 40 + 9 (x + 3)^2 + y^2 = 49 Center = (-3, 0) Radius = 7 Problem 22: x^2 + y^2 - 2x + 4y = 76 x^2 - 2x + 1 + y^2 + 4y + 4 = 76 + 1 + 4 (x - 1)^2 + (y + 2)^2 = 81 Center = (1, -2) Radius = 9