F(x) = 2x^2 − 3x − 5 Part A: What are the x-intercepts of the graph of f(x)? Show your work.

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.

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.

 Answer  is in the steps..

Step-by-step explanation:

f(x)= - 3x -5        

A) To find the x intercepts of a parabola we have to set the whole equation equal zero because the x intercept is when y equal zero in other words where f(x) equal zero.

   - 3x - 5 = 0     Now solve using quadratic formula.

  x = -b±    

  x = 3 ±  

   x = 3 ±  / 2a

   x= 3 ± 7 /4

   x= -1   or x = 5/2  

The x intercepts are  (5/2,0)  and (-1,0)

B)  The graph vertex of the graph of f(x)  is going to be at a minimum because the leading coefficient of the function has a positive integer which means the parabola will open up and its vertex will be at the minimum point.

 Using the  x coordinates  we could find their average and find the x coordinate of the   vertex.

 =   = 3/4  

The x coordinate of the vertex  is 3/4 so we will input that into the equation and solve for the y coordinate  

  = 18/16 - 9/4 -5  =  -49/8

The y coordinate of the vertex  is  -49/8

So the vertex is (3/4, -49/8)  

C)   First  I will graph the vertex and then graph he two x intercepts and connect then like a U shape.