An expression is shown below: f(x) = 4x^2 − 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 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)

The answer to your question is:

Part A:  x₁ = 3   x₂ = -5/4

Part B. Vertex = (7/8, - 18.06)                                  

Step-by-step explanation:

Data

                                   4x² - 7x - 15

Part A. Factor the expression given to find the x - intercepts.

                   - Multiply 4 by -15 = -60

                   - Find the prime factors of -60

                       -60   2

                      -30    2

                     - 15     3

                       -5     5

                       -1

                    - Find to numbers that add them up give -7

                      these numbers are -12 and + 5                  

                                   4x² - 12x + 5x - 15

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

                                   (x - 3)(4x + 5)

                     - Equal each term to zero to find the x-intercepts

                       x₁ = 3                x₂ = -5/4

Part B. The vertex is a minimum

                                  y =   4x² - 7x - 15

                                 y + 15 + 4(7/8)² = 4(x² - 7/4 x + (7/8)²)

                                 y + 289/16 = 4( x - 7/8)²

Vertex = (7/8, - 18.06)      

Part  C.

1.- Plot the the vertex

2.- Plot the x- intercepts

3.- Join the points                          

astronomers is your final answer! : )