An expression is shown below:
f(x) = –16x2 + 24x + 16
part a: what are the x-intercepts of the graph of f(x)? show your work. (2 points)
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)

Xint
set equal to zero and solve since when y=0, that is when line crosses x axis

0=-16x^2+24x+16
undistribute -8
0=-8(2x^2-3x-2)
we conclude that 2x^2-3x-2=0 because if we have -8x=0, we conclude that x=0

0=2x^2-3x-2
factor
0=(x-2)(2x+1)
set to zero
x-2=0
x=2
2x+1=0
x=-1/2

x intercept are at (2,0) and (-1/2,0)


we know that this is a parabola and parbolas normally open up
vertex is max, because leading term (term before the x^2 term) is negative
if it
vertex is -b/2a when  you have ax^2+bx+c=f(x)

a=-16
b=24
-24/(2*-16)=-24/-32=3/4
x coordinate is 3/4
sub for x to fnd  cordinate
f(3/4)=-16(3/4)^2+24(3/4)+16
f(3/4)=-16(9/16)+18+16
f(3/4)=-9+34
f(3/4)=25
vertex coordinate is (3/4,25)


graph vertex and x intercepts and draw a line with vertex as max and going through the x intercepts

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