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 $y=x^2-8x+9$.