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)

A) (3, 0) and (-1.25, 0)

B) minimum

(0.875, -18.063)

C) see picture attached

Step-by-step explanation:

f(x) = 4x² − 7x − 15

A) Using quadratic formula:

B) The x-coordinate of the vertex is located at:

x = -b/(2a)

x = 7/(2*4) = 0.875

To find the y-coordinate of the vertex, just replace the x value previously found into f(x), as follows:

f(x) = 4(0.875)² − 7(0.875) − 15 = -18.063

The vertex is going to be a minimum becauseI a (the leading coefficient) is positive, which means that the curve opens upward.

C) Locate the three previous points on the plane. Draw a U-shape curve that passes through them.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.