Question

What is the y-value of the vertex of the function f(x) = –(x + 8)(x – 14)?
The y-value of the vertex is......

Answer 1

@Directrix do you know this one

Answer 2

@Secret-Ninja

Answer 3

@pitamar

Answer 4

Well, since we can find the roots for this equation, we can basically tell that the vertex is in the middle.
The roots would be the x-intercepts. the points where y=0. We can tell those 2 easily in the form you put it because:
$$
f(-8) = -(-8+8)(-8-14) = -(0)(-8-14) = 0 \\
f(14) = -(14+8)(14-14) = -(14+8)(0) = 0
$$
So the roots are at x=-8 and x=14. The 'x' which is in the middle of those two would be:
$$
\frac{-8+14}{2} = \frac{6}{2} = 3
$$
So the vertex will be at point x=3. Now we can find the 'y' value at that point:
$$
f(3) = -(3+8)(3-14) = -(11)(-11) = 11^2 = 121
$$
And just to check:
http://www.wolframalpha.com/input/?i=%20%E2%80%93(x%20%2B%208)(x%20%E2%80%93%2014)
As you can see the max point (which is our vertex here) is at (3,121)

Answer 5

Great explanation!

@pitamar

Answer 6

Thanks =)

Answer 7

wow youre great thank you @pitamar

Answer 8

wait so the answer is 3? @pitamar

Answer 9

The vertex is at x=3, but you are asked to give the 'y' value at that point, which would be the f(3)

Answer 10

hmmm im confused now sorry but can you explain a more @pitamar

Answer 11

ok, what is confusing you? what they mean by 'y' perhaps?

Answer 12

im confused on how to get the answer like do i have to solve @pitamar

Answer 13

Well, y = f(x). That's why it is not explicitly shown up above. but basically, if you can find the value of f(x) then you found 'y', they are the same.
For example, say I have the function:
$$ f(x) = 2x+1 $$ It could be written as
$$
y = 2x + 1
$$ Now if i'm told that \(x=5\), since 'y' is defined by 'x' I can find it:
$$
f(5) = 2\cdot 5 + 1 = 10 + 1 = 11 \\
y =11
$$
Do you understand this example?

Answer 14

okay i understand now so i have to put some number f() in between but how do i know what number to use @pitamar

Answer 15

you know that the vertex is at point x=3. That would be the 'maximum' point in our specific function.
That means that f(3) will be greater than any other f(x).
That's good, but they want to know what is the 'y value' of the vertex. means, what is that 'maximum' value.
We know at what point we have that maximum value (x=3), so now we just need to compute the value with f(3)

Answer 16

so it would be like this f(3)=-(3+8)(3-14) @pitamar

Answer 17

ye =]

Answer 18

and all i have to do is solve it now? @pitamar

Answer 19

ye

Answer 20

so the answer is -121 @pitamar

Answer 21

close. look at my first answer again. It includes this part and it will make more sense now =)

Answer 22

oh so its just 121 @pitamar

Answer 23

Yes exactly

Answer 24

thank you so much @pitamar

Answer 25

Sure np