Question

Please help solve this

Answer 1

`(-1, -16)`

Explanation:

First, we can expand the right side of this equation.

`y=(x + 5)(x-3)`

`y = x^2 -3x + 5x - 15`

`y = x^2 + 2x - 15`

Then, we can move the 15 to the left side.

`y + 15 = x^2 + 2x`

Now, the equation is in a form where we can complete the square for x. Remember that anything we add to one side, we also have to add to the other side.

`y + 15 + (2/2)^2 = x^2 + 2x + (2/2)^2`

`y + 16 = x^2 + 2x + 1`

`y + 16 = (x+1)^2`

Finally, we can move the 16 to the right side.

`\boxed{y = (x+1)^2 - 16}`

The equation of the parabola is now in vertex form:

`y = (x - h)^2 + k`,

where
`(h,k)` is the vertex of the parabola.

In the equation we just solved for (
`y = (x+1)^2 - 16`), we can identify the following:

• 
  `h = -1`
• 
  `k = -16`

Therefore, the vertex of the parabola is:

`\boxed{(-1, -16)}`