Write an equation for the parabola whose vertex is at (3, 6) and which
passes through (4, 4).

The vertex of a parabola is the maximum or the minimum point on the parabola.

The equation of the parabola is:

The given parameters are:

The equation of parabola is:

Substitute values for x, y, h and k

Subtract 6 from both sides

Substitute values for h, k and a in

Hence, the equation of the parabola is:

Read more about parabolas at:

link

Step-by-step explanation:

The vertex form of the equation of the parabola with vertex (h, k)  is:

f(x) = a(x - h)² + k

so the equation of parabola with the vertex (3, 6) is

f(x) = a(x - 3)² + 6  

passes through the point (4, 4) means: if x=4 then f(x)=4

4 = a(4 - 3)² + 6  

4 -6 = a(1)² + 6 -6

-2 = a

Therefore the equation of parabla is:

                                  f(x) = -2 (x - 3)² + 6  

89

step-by-step explanation: