Question

What is the vertex of `y= (x+8)^2-2x-6`?

Answer 1

See the solution below

Explanation:

`y = x^2 + 16x + 64 -2x -6`
`y = x^2 + 14x + 58`

Since the equation is quadratic, Its graph would be a parabola.
graph{x^2 + 14x + 58 [-42.17, 37.83, -15.52, 24.48]}

As you can see from the graph that the roots are complex for this quadratic equation.

The vertex can be found out by the following formula,
`(x,y) = (-b/(2a) , -D/(4a))`

where,
`D =` discriminant

Also
`D = b^2 - 4ac`

here,
`b = 14`
`c = 58`
`a = 1`

Plugging in the values

`D = 196 - 4(58)(1)`
`D = 196 - 232`
`D = -36`

Therefore the vertex is given by
`(x,y) = (-14/(2) , 36/4)`
`(x,y) = (-7 , 9)`