PLEASE HELP ASAP
Use the function f(x) = 2x2 − x − 10 to answer the questions. Part A: Completely factor f(x). (2 points) Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) Part C: Describe the end behavior of the graph of f(x). Explain. (2 points) Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)

Part A: (2x−5)(x+2)

Part B: (5/2,0) and (-2,0)

Part C: The graph of f(x) has both "ends" of the graph pointing upward. You can describe this as heading toward infinity.

Part D: To graph function we can use x-intercepts and "ends" to sketch.In order to graph better use one more point of parabola that you can find as the average of x-intercepts: (-2+5/2)/2 =1/4.This is just x coordinate and you need to plug in 1/4 in the f(x) and find y coordinate -10 1/8. You can use y-intercept (0,-10) as well to graph.

Step-by-step explanation:

Part A:  

What 2 numbers when multiplied give -20 and when added up -1. Numbers are -5 and 4.

Rewrite quadratic expression as

Factor by grouping

Part B: x- intercepts are found when (2x−5)(x+2) = 0

Set factors equal to 0.

2x−5=0 or x+2=0

x=5/2 or x=−2

Part C: The lead coefficient (multiplier on the ) is a positive number, which causes the parabola to open upward.The first graph of has both "ends" of the graph pointing upward so  this can be described as heading toward infinity.

Part D:

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints