Please help Use the function f(x) to answer the questions.

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 a 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)

Step-by-step explanation:

1) we have to solve the associated equation

-16x^2 + 24x + 16 = 0

-2x^2 + 3x + 2 = 0

2x^2 -3x -2 = 0

Δ = 9 + 16 = 25

x1 = (3 + 5)/4= 2

x2 = (3 - 5)/4 =-1/2

the x intercepts are -1/2 and 2

2) a maximum because the parabola opens downwards (the first term is negative)

V(x) = -b/2a = -24/-32 = 3/4

V(y) = -16(9/16) + 24(3/4) + 16 = -9+18 + 16 = 25

V(3/4,25)

3) for draw a parabola is are necessary the coordinates of the vertex and of two points: one that lies to left of the vertex, and one that lies on the right to the vertex.

So we already have the necessary informations to draw it.

"a" determine whether sage found the correct quotient. show your work

step-by-step explanation: