Put the quadratic into vertex form and state the coordinates of the vertex.
y=x 2−8x−48
Vertex Form: y, equalsy=
Vertex: left bracket(
,
right bracket)
To put the quadratic function into vertex form, we need to complete the square.
y = x^2 - 8x - 48
First, let's group the terms in a way that allows us to complete the square:
y = (x^2 - 8x) - 48
Next, we need to take half of the coefficient of x, square it, and add it to both sides of the equation:
y + 64 = (x^2 - 8x + 16) - 48 + 64
Simplifying further:
y + 64 = (x - 4)^2 + 16
Finally, subtract 64 from both sides of the equation to isolate y:
y = (x - 4)^2 - 48
Therefore, the quadratic function in vertex form is:
y = (x - 4)^2 - 48
The coordinates of the vertex are (4, -48).