Question

What is the y-value of the vertex of the function f(x) = –(x – 3)(x + 11)?

The y-value of the vertex is

Answer 1

You can factor it out to get -x^2-8x+33, since the x of vertex is -b/2a, the x coordinate is -4, and plug it back in you would get 49

Answer 2

49.

Explanation:

We have been a function
`f(x)=-(x-3)(x+11)`. We are asked to find the y-value of vertex of the given function.

Upon multiplying both factors, we will get,

`f(x)=-(x*x+11*x-3*x-3*11)`

`f(x)=-(x^2+11x-3x-33)`

`f(x)=-(x^2+8x-33)`

`f(x)=-x^2-8x+33`

Now, we will use
`(-b)/(2a)` formula to find the x-coordinate of vertex of parabola.

`(--8)/(2*-1)`

`(8)/(-2)`

`-4`

Since the x-coordinate of vertex of parabola is
`-4`, so we will substitute
`x=-4` in our equation to find y-coordinate of parabola.

`f(-4)=-(-4)^2-8(-4)+33`

`f(-4)=-16+32+33`

`f(-4)=49`

Therefore, the y-coordinate of vertex of the given parabola is 49.