Question

Find the Maximum y-value on the f(x)
f(x)= -x^2+4x+9

Answer 1

@HawkCrimson I can't remember if you helped me last time or not?

Answer 2

Do you recognize that this is a parabola which is concave downward?

Answer 3

No?

Answer 4

leading coefficient is negative ( it is -1) so the parabola opens down

Answer 5

okay, that makes sense but putting that in a formula how do you figure it out? by x= -b/2a?

Answer 6

maximum is the second coordinate of the vertex
the first coordinate of the vertex of \(y=ax^2+bx+c\) is always \(-\frac{b}{2a}\)

Answer 7

in your case it is \(-\frac{4}{2\times (-1)}=2\)

Answer 8

second coordinate of the vertex, which is what you are looking for, is what you get when you replace \(x\) by \(2\)

Answer 9

-4/ 2(4)= -4/6 = -2/3? Or is that completely wrong?

Answer 10

or do you bring it back to the equation of 2^2+4*(2)+9

Answer 11

which if I am correct gives you a max of 25