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

Question

asked May 28, 2022 123k views

1 Answer

Sergey Aldoukhov · Answer 1 · 2022-05-31T23:28:12+0000

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
.