An expression is shown below: f(x) = −16x2 + 60x + 16

Part A: What are the x-intercepts of the graph of the 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)

Good evening,

Step-by-step explanation:

f(x) = −16x2 + 60x + 16

Part A: x-intercepts

−16x2 + 60x + 16 = 0

⇔ -4(4x²-15x-4) = 0

⇔ -4[(4x²-16x) + (x-4)] = 0

⇔ -4[4x(x-4) + (x-4)] = 0

⇔ -4(x-4)(4x+1) = 0

⇔ x = 4 or x = -1/4

part B:

since the coefficient of -16x² is -16 which is negative number then the function has a maximum at the point ( -60/2(-16)  ,  f(-60/2(-16)) ) = (15/8 , 289/4).

partC:

first we plot the maximum point then plot x-intercepts 2 points

then we draw the graph.

look at the photo below for the graph.

:)