Question

Algebra 1 help please!!!
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)

Answer 1

These are fun! Are you familiar with completing the square to find your vertex and stuff?

Answer 2

I do remember learning about it but I can't seem to remember at the moment. Can you explain please?

Answer 3

I will do the problem step by step, explaining along the way what I am doing, ok?

Answer 4

Alright

Answer 5

part A: The x intercepts come from factoring the problem and finding where x = 0. Factor that out. BRB with a factored form.

Answer 6

Ok, the factored form of that gives you the following:
-4(x-4)(x+1/4). Setting each of these equal to zero, we have x-4=0 and x+1/4=0. Solving for x we get that x = 4 and x = -1/4. Those are your x intercepts. In other words, those are the points on the x axis where the graph will go through it. Like this, sort of: