Question

The graph of a quadratic function has a vertex at (5,3) and goes through the point (-1,-9). What is the equation of the function?

Answer 1

`y=-(1)/(3) (x-5)^2+3`

Explanation:

We are given the following;

• Vertex of a quadratic function = (5,3)
• A point where the function passes through (-1, -9)

Required to determine the equation of the function;

• We need to know the vertex form of a quadratic function is;

`y=a(x-h)^2+k`, where h and k correspond to the vertex (h,k)

• Therefore, we can replace the variables h and k of the vertex in the equation;

That is;

`y=a(x-5)^2+3`

Then we use the equation and the point given to solve for a

x = -1 and y = -9

We get;

`-9=a(-1-5)^2+3\\-9 = a(36) + 3\\-9 - 3 = 36a\\-12 =36a \\a=-(1)/(3)`

Substituting the values of a, h and k in the equation, we get;

`y=-(1)/(3) (x-5)^2+3`

Thus, the equation of the function in the vertex form is
`y=-(1)/(3) (x-5)^2+3`