Question

Determine, as exact values, the x and y-intercepts of the graph of the following functions

a) f(x) = -3(x+2)^2+3

b) f(x) = 2(x-6)^2-6

c) f(x) = -1/4(x+1)^2+5

Answer 1

For the y-intercept let x = 0 in each of the given functions, so that is easy
I will do a)
f(x) = -3(x+2)^2+3
f(0) = -3(0+2)^2 + 3 = -9 , so the y-intercept is -9

For the x-intercept, let f(x) = 0 or y = 0 if written in that form
a)
-3(x+2)^2+3 = 0
-3(x+2)^2 = -3
(x+2)^2 = 1
x+2 = ± √1 = ± 1
x = -1 or x = -3

verification:
www.wolframalpha.com/input/?i=plot+f(x)+%3D+-3(x%2B2)%5E2%2B3+from+-4+to+1