Question

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

Answer 1

Answer:

           f(x) = -2 (x - 3)² + 6

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  

Answer 2

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

The equation of the parabola is: $\mathbf{y = -2(x -3)^2 + 6}$

The given parameters are:

$\mathbf{Point = (x,y) =(4,4)}$

$\mathbf{Vertex = (h,k) =(3,6)}$

The equation of parabola is:

$\mathbf{y = a(x - h)^2 + k}$

Substitute values for x, y, h and k

$\mathbf{4 = a(4 - 3)^2 + 6}$

$\mathbf{4 = a(1)^2 + 6}$

$\mathbf{4 = a + 6}$

Subtract 6 from both sides

$\mathbf{a = -2}$

Substitute values for h, k and a in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = -2(x -3)^2 + 6}$

Hence, the equation of the parabola is:

$\mathbf{y = -2(x -3)^2 + 6}$

Read more about parabolas at:

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