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.

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the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point