Question

What is the vertex of # y= –x^2 +12x – 4?

Answer 1

`color(blue)("Vertex"->(x,y)->(6,32)`

Explanation:

`color(blue)("General condition")`

Consider the standard form of `y=ax^2+bx+c)`

Write this as `y=a(x^2+b/ax)+c`

`x_("vertex")=(-1/2)xxb/a`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Solving your question")`

In your case `a= -1 and b=12 ->x_("vertex")=(-1/2)xx12/(-1) = +6`

Substitute `x=6 -> y_("vertex")=32`

`color(blue)("Vertex"->(x,y)->(6,32))`