2. Start with the quadratic function: f(x) = ax² +bx+c and follow the steps below. 62 (a) Step 1: Show that f(x) (x + 2)² − b 2 + c - a 2a Assume that a 0. Hint: We did something like this when solving for the quadratic roots formula. = (b) Step 2: That part of (a) that depends on x is given by (x + 2)². We want to f(x) a study exactly how (x + 2)² depends upon x. Show that: i. (x+)² ≥ 0 for all values of ii. (x + 2)² = 0 only when x = - so (x + 2)² = 0 has 2 identical roots equal 2a 2a to b 2a b +h. 2a iii. This is an interesting result. Suppose that h is a positive number, it can be large of small. Show that (x + 2)² takes the value h² when x = Next show that (x + 2)² takes the value h² when x = h. Using a diagram show that this means that (x + 2)² is symmetric about x = - It behaves just like the function x² and we know x² is symmetric about x = 0. 2a
2. Start with the quadratic function: f(x) = ax² +bx+c and follow the steps below. 62 (a) Step 1: Show that f(x) (x + 2)² − b 2 + c - a 2a Assume that a 0. Hint: We did something like this when solving for the quadratic roots formula. = (b) Step 2: That part of (a) that depends on x is given by (x + 2)². We want to f(x) a study exactly how (x + 2)² depends upon x. Show that: i. (x+)² ≥ 0 for all values of ii. (x + 2)² = 0 only when x = - so (x + 2)² = 0 has 2 identical roots equal 2a 2a to b 2a b +h. 2a iii. This is an interesting result. Suppose that h is a positive number, it can be large of small. Show that (x + 2)² takes the value h² when x = Next show that (x + 2)² takes the value h² when x = h. Using a diagram show that this means that (x + 2)² is symmetric about x = - It behaves just like the function x² and we know x² is symmetric about x = 0. 2a
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.2: Transformations Of Quadratic Functions
Problem 50PFA
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