Chapter 6, Section 6.1, Question 036

Question

The function g(x) is obtained by shifting the graph of y=x^2

If g(3) = 25

(a) g is the result of applying only a horizontal shift to y=x^2

g(x) =


(b) g is the result of applying only a vertical shift to y=x^2

g(x) =

g left-parenthesis x right-parenthesis equals

(c) g is the result of applying a horizontal shift right 2 units and an appropriate vertical shift of y=x^2

g(x) =

Answer 1

(a) 5^2 = 25, and we want
(3-h)^2 = 25
so, 3-h = ±5
g(x) = (x+2)^2 or (x-8)^2

(b) g(x) = x^2+16

(c) shift right 2 is (x-2)^2
Since (3-2)^2 = 1,
g(x) (x-2)^2 + 24