(08.07 HC)
An expression is shown below:

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 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)

(10 points)

A) x = (-1/2) and x = 2,

B) x = 3/4, y= 25 (3/4,25) Its a maximum because the vertex is higher than the x coordinates. What i mean by that is that the vertex is at y coordinate 25 and then at x= 2, y = 0 it means its a maximum.

C) You have the vertex and the y- intercepts. You have 3 points in order to draw the graph.

Step-by-step explanation:

Note that in order to find number 1, you will have to use the quadratic formula. However, I cheated and used wolframalpha but you can also use it to double check. I am sure that if you used the quadratic formula you will get the same roots.

Hope this helps.

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)