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

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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