Ialready did part a (if i was right) can you with b and c? !

an expression is shown below:

f(x) = –16x^2 + 60x + 16

part a: what are the x-intercepts of the graph of the f(x)? show your work. (2 points)

first i factor out the gcfs (the same as i did in question 2 part a):
f(x) = –16x^2 + 60x + 16
f(x) = (–16x^2 - 4x)(64x + 16)
f(x) = -4x(4x + 1)16(4x + 1)
then i substituted 0 for f(x):
0 = -4x(4x + 1) 16(4x + 1)
and solved for the x's:
0 = -4(0)(4(-0.25) + 1) 16(4(-0.25 + 1)

part b: 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. (3 points)

part c: what are the steps you would use to graph f(x)? justify that you can use the answers obtained in part a and part b to draw the graph. (5 points)

Part A
f(x) = 0
-16x^2 + 60x + 16 = 0
-16x^2 - 4x + 64x + 16 = 0
(-16x^2 - 4x) + (64x + 16) = 0
-4x(4x + 1) + 16(4x + 1) = 0
(-4x+16)(4x + 1) = 0
-4(x - 4)(4x + 1) = 0
x-4 = 0 or 4x+1 = 0
x = 4 or x = -1/4 = -0.25

The two x intercepts are x = 4 and x = -0.25. This means the graph crosses the x axis at (4,0) and (-0.25, 0)

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Part B

y = -16x^2 + 60x + 16 is in the form y = ax^2 + bx + c where
a = -16
b = 60
c = 16

The x coordinate of the vertex (h) is 
h = -b/(2a)
h = -60/(2*(-16))
h = 1.875

Plug this into the original function to find the y coordinate of the vertex
y = -16x^2 + 60x + 16
y = -16(1.875)^2 + 60(1.875) + 16
y = 72.25

Therefore the vertex is (h,k) = (1.875, 72.25)

This is the highest point on the graph. How can we know this without graphing? Notice how a = -16 which is negative. Since a < 0, this means the parabola opens down (think negative as a frowny face). The vertex is at the peak of the upside down parabola. 

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Part C

To graph this parabola, generate a bunch of points to plot. To get any individual point, you plug in an x value to get a corresponding y value

For example, if x = 0, then
y = -16x^2 + 60x + 16
y = -16(0)^2 + 60(0) + 16
y = 16
so (0,16) is one point on the graph

If x = 1, then
y = -16x^2 + 60x + 16
y = -16(1)^2 + 60(1) + 16
y = 60
making (1,60) another point on the curve. 

With enough points, the better and more accurate the drawing is. The curve will go through all the points found. 

See the attachment to see what the graph looks like. Specifically the x intercepts and vertex.