$$f(x) = -16x^2 + 60x + 16$$

Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.

Question

$$f(x) = -16x^2 + 60x + 16$$

Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.

jtvatsim · Answer

First part of the answer is clear. Second, can be found quickly with Calculus.

camerondoherty · Answer

Calculus? I'm only in Alg 1. Haha

jtvatsim · Answer

But Calculus makes the world go round. :)  It's still possible to solve. Let's see what the others suggest.

camerondoherty · Answer

And I have no idea of the first part 
It may be clear to you but its definately not clear to me cx

jtvatsim · Answer

haha... I know, I was assuming too much. :P

jtvatsim · Answer

Do you know what shape the graph will be?

triciaal · Answer

standard form  ax^2 + bx + c = 0
vertex form    a(x-h)^2 + k = 0
x-coordinate of the vertex h = -b/2a
y value for vertex  = result for f(h)

camerondoherty · Answer

Wait, so...
what is a, b, c, x, and k? cx

camerondoherty · Answer

Like, do I sub in anything

triciaal · Answer

since you are not ready for calculus, pick 2 points one on each side of the vertex and use this as the x value in f(x) and calculate the y values
 you will be able to do a sketch (x, y) and determine if the vertex was a maximum or minimum

camerondoherty · Answer

So, do I graph it on desmos and pick two points?

triciaal · Answer

do you know how to factorize the equation given?

camerondoherty · Answer

Yep

camerondoherty · Answer

I actually already did
4(x - 4)(4x + 1)

camerondoherty · Answer

before

triciaal · Answer

the vertex of the equation is when the function = 0
same as saying when y = 0 
find the x-values

camerondoherty · Answer

I had already found those as well cx
I got 4 and -1/4

triciaal · Answer

great 
so when y = 0 what are the x values?

camerondoherty · Answer

the zeroes

triciaal · Answer

so the points are (x, y) and y = 0

camerondoherty · Answer

(4,0) & (-1/4,0)

camerondoherty · Answer

Ohhhh, and those are the vertex coordinates?

camerondoherty · Answer

I still don't get how it is a maximum though :/

triciaal · Answer

correction to this post thanks@jtvatsim
the vertex of the equation is when the function = 0 same as saying when y = 0 find the x-values 

the original is correct  -b/2a =h the x-coordinate

camerondoherty · Answer

Wait, what? cx

jtvatsim · Answer

I'll draw the picture of where we are at right now...|dw:1418696078251:dw|