Question

Find the vertex of the graph of the function.

f(x) = 4x2 + 24x + 32

Answer 1

the vertex lines on the axes of symmetry for a parabola, so first you want to find that and you can do so by using axes of symmetry = -b/2a
where y = ax^2 + bx + c

Answer 2

lies*

Answer 3

f(x) = 4x2 + 24x + 32
b=24 a=4
-b/2a
-24/8

Answer 4

yup thats correct! so now to find the y coordinate that goes with this, we simply sub -24/8 = -3, into the equation, to solve for y

Answer 5

Hmm how did you get the -3 ?
Sorry I'm really bad at math !!

Answer 6

Oh thats okay! I just simplified -24/3 because 3 goes into 24, 8 times and we have a minus out the front as well... @ashhhrodriguez

Answer 7

Oh WOW thank you!
What exactly do I sub 3 for all the x values ?

Answer 8

I mean -3!

Answer 9

okay so we know that at our axes of symmetry, x = -3, right?

Answer 10

Now we want to sub this back into the equation, to find out what y is equal to as x = -3... agreed?

Answer 11

Ohh so we already have our x value to our vertex -3

Answer 12

yuppp thats what the equation -b/2a gave us

Answer 13

so now we have to find the y value which goes with it

Answer 14

and we can do that by subbing x = -3 back into the original equation

Answer 15

(-3,-4) Thank you so so much !

Answer 16

Yup thats correct! And no problem! :)