Question

Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (8,12) and has (6,10) as its vertex. What is the standard form of the equation? A) The vertex form of the equation is f(x) = 1 2 (x - 6)2 + 10. The standard form of the equation is f(x) = 1 2 x2 - 6x + 28. B) The vertex form of the equation is f(x) = 1 2 (x + 6)2 + 10. The standard form of the equation is f(x) = 1 2 x2 + 6x + 28. C) The vertex form of the equation is f(x) = 1 2 (x - 6)2 - 10. The standard form of the equation is f(x) = 1 2 x2 - 6x - 28. D) The vertex form of the equation is f(x) = − 1 2 (x - 6)2 + 10. The standard form of the equation is f(x) = − 1 2 x2 - 6x + 28.

Answer 1

f(x) = a(x-h)^2 + k, for a parabola that passes through the point (8,12) and has (6,10) as its vertex: 

Start with     y =f(x) = a(x-h)2 + k.    We know that (8,12) and (6,10) are both on the graph of the parabola, and that (6,10) is the vertex.  Therefore the following is
true:
 
 f(x) = y = a(x-6)^2 + 10     =>     12= y = a(8-6)^2 + 10

Then 12 = a(2)^2 + 10, or 2 = a(4), or a = 2/4, or a = 1/2.

Then the equation for this parabola is  y = (1/2)(x-6)^2 + 10.