What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (1, −7) and has (2, 3) as its vertex. what is the standard form of the equation? a. vertex form: f(x) = 10(x + 4)2 + 5 standard form: f(x) = −10x2 + 40x + 165 b. vertex form: f(x) = −6(x − 4)2 + 3 standard form: f(x) = −6x2 + 7x − 24 c. vertex form: f(x) = −10(x − 2)2 + 3 standard form: f(x) = −10x2 + 40x − 37 d. vertex form: f(x) = −3(x − 2)2 + 4 standard form: f(x) = −3x2 + 12x +16?

In Vertex form h and k represent the point where the vertex is at. h is the opposite sign value for the X-point value. and k is the Y-point value.
So since the vertex is (2,3) the X-value is the opposite sing on +2 (which is -2). 
Looking at out options, a and b can be eliminated because they have +4 and -4 where h is.
At the vertex point (2, 3) 3 is the Y value point. So it should be adding +3. This eliminates d.

To make sure c is the correct answer we can find the number that is supposed to go in front of the parenthesis by plugging in the X and Y values of the other point (1, -7) into the X and Y spots:
-7=?(1-2)^2+3
-Subtract 3-
-10=?(-1)^2
(-1 squared is 1)
-10=?

C is the correct answer.