Please help :( Use the function f(x) to answer the questions.
f(x) = −16x2 + 22x + 3

Part A: What are the x-intercepts of the graph of f(x)? Show your work.

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.

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.

Step-by-step explanation:

Part A

We have to solve the associated equation

-16x^2+ 22x + 3 = 0

Δ/4 = 121 + 48 = 169

x1 = (-11 -13)/-16 = 3/2

x2= (-11 + 13)/-16 = -1/8

(-1/8,0) ; (3/2,0)

Part B

the vertex is a maximun because the parabola opens downwards. We can say this because the term that multiply x^2 is negative

V(x) = -b/2a = -22/-32 = 11/16

V(y) =  -16(11/16)^2 + 22(11/16) + 3  = -16(121/256) + 121/8 + 3 = -121/16 + 121/8 + 3 = (-121 + 242 + 48)/16 = 169/16

V:  (11/16,169/16)

Partc C

for graph a parabola are necessary three points: the vertex and two points that lies on opposite parts of the symmetry axis of the parabola.

So we can say that with the points found in Part A and Part B we can already draw it.

In fact the axis of symmetry is x = 11/16 and the x intercepts lies on opposite parts of it and we also found the vertex