Question

Write the equation of a quadratic function who has the vertex of (4,-7)

Answer 1

Given:

The vertex of a quadratic function is (4,-7).

To find:

The equation of the quadratic function.

Solution:

The vertex form of a quadratic function is:

`y=a(x-h)^2+k` ...(i)

Where a is a constant and (h,k) is vertex.

The vertex is at point (4,-7).

Putting h=4 and k=-7 in (i), we get

`y=a(x-4)^2+(-7)`

`y=a(x-4)^2-7`

The required equation of the quadratic function is
`y=a(x-4)^2-7` where, a is a constant.

Putting a=1, we get

`y=(1)(x-4)^2-7`

`y=(x^2-8x+16)-7`
`[\because (a-b)^2=a^2-2ab+b^2]`

`y=x^2-8x+9`

Therefore, the required quadratic function is
`y=x^2-8x+9`.