The graph of function g is a parabola with the vertex located at (5, 9). The parabola also passes through the point (3, 1). Which of the following is an equation in vertex form for this function?
a) g(x) = 2(x – 5)^2 + 9
b) g(x) = 2(x – 5)^2 – 9
c) g(x) = 2(x – 5)^2 – 9
d) g(x) = –2(x + 5)^2 + 9

A

Step-by-step explanation: vertex is (-H,k)

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1