If fx 4x2 4 and gx x a find a so that the graph of f g cr

If f(x) = 4x^2 +4 and g(x) = x + a, find a so that the graph of f g crosses the y-axis at 20. What is the value of a? (Use reduced fractions or integers Use commas to separate values.)

Solution

f(x) = 4x^2 + 4

g(x) = x + a

fog = f(g(x))

fog = 4(x + a)^2 + 4

fog = 4x^2 + 8ax + 4a^2 + 4

given that when x = 0, y = 20

f(g(0)) = 20

20 = 4*0^2 + 8*a*0 + 4*a^2 + 4

20 = 4*a^2 + 4

4*a^2 = 16

a^2 = 4

a = sqrt 4

a = +2 OR -2