Answer:
[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}[/tex]
Step-by-step explanation:
To find y-intercept of a graph, we have to substitute x = 0 to find it - consider each functions:
First Choice
[tex]\displaystyle{f(x) = 2x(x+14)-64}\\\\\displaystyle{f(0) = 2\cdot 0(0+14)-64}\\\\\displaystyle{f(0) = 0\cdot 14-64}\\\\\displaystyle{f(0) = -64}[/tex]
Second Choice
[tex]\displaystyle{f(x) = (x+4)^2+2x}\\\\\displaystyle{f(0) = (0+4)^2 + 2(0)}\\\\\displaystyle{f(0) = 4^2}\\\\\displaystyle{f(0) = 16}[/tex]
Third Choice
[tex]\displaystyle{f(x) = (x-16)^2 + 4}\\\\\displaystyle{f(0) = (0-16)^2 + 4}\\\\\displaystyle{f(0) = (-16)^2 + 4}\\\\\displaystyle{f(0) = 256 + 4}\\\\\displaystyle{f(0) = 260}[/tex]
Fourth Choice
[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}\\\\\displaystyle{f(0) = -2(0-3)^2 + 2}\\\\\displaystyle{f(0) = -2(-3)^2 + 2}\\\\\displaystyle{f(0) = -2\cdot 9 + 2}\\\\\displaystyle{f(0) = -18+2}\\\\\displaystyle{f(0) = -16}\\[/tex]
Therefore, fourth choice is correct.
