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                          

"The Maori: Genealogies and Origins in New Zealand" and "The Raven and the First Men: The Beginnings of the Haida" are very similar myths, but at the same time very different from each other. The similarity between them is perceived through the subject that governs their narratives. This is because both myths are in charge of telling, each in its own way, the origin of human beings and the planet that houses them. However, the myth "The Maori" presents this narrative with courage as its main theme, since it narrates a sequence of struggles and conflicts that resulted in the creation of the world and humans. The myth "The Raven", on the other hand, does not base the creation of the world and humans on situations of courage, but on pleasure and satisfaction of desires.