Question

100 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!! PLEASE SHOW STEPS TO ALL PARTS

Use the function f(x) to answer the questions:

f(x) = 4x2 − 7x − 15

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)

Answer 1

Part A & B

Step-by-step explanatPart A:

f(x) = 4x ^ 2 - 7x - 15

0 = 4x ^ 2 - 7x - 15

a = 4, b = -7, c = -15

a x c = -60

-12 x 5 = -60

-12 + 5 = -7

(4x + 5)(4x - 12)

4x ^ 2 - 12x I + 5x - 15

4x(x - 3) + 5(x - 3)

(x - 3)(4x + 5)

x = 3 x = -1.25 or -5/4

Part B:

Minimum point

(x1 + x2)/2

(3 -1.25)/2 = 0.875

f(x) = 4x ^ 2 - 7x - 15

f(0.875) = 4(0.875) ^ 2 - 7(0.875) - 15

f(0.875) = 3.06 - 6.125 - 15

f(0.875) = -18.065ion: