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

@HelpMEEE
Do you still need a response to this question?

Answer 2

yes please

Answer 3

These (including your other questions) relate to properties of parabolas.
Have you studied the properties of parabolas?

Answer 4

In the case of a parabola equation in its vertex form:
y=a(x-h)^2+k,
then (h,k) is the vertex of the parabola, AND vice versa.
If a>0, it opens up, and if a<0, the parabola opens down.

As you probably already know, the line of symmetry of a parabola passes through the vertex.
For example,
y=2(x-2)+7,
the vertex is at (2,7), and the (vertical) line of symmetry passes through (2,7), which makes the line of symmetry x=2.

Next, since a parabola is symmetric about its vertex, the zeroes of a parabola are equidistant from the vertex.
This means that in an equation (not in vertex form) in factored form:
y=(x-4)(x-8)
the zeroes are at (x-4)=0, or x=4, similarly x=8.
Since {4,8} are the zeroes of the parabola, the line of symmetry is
x=(4+8)/2=6 due to symmetry.
The y-value of the vertex can be obtained by putting x=6 into the parabola equation, namely
y=(6-4)(6-8)=2(-2)=-4.