Use the function f(x) = 2x2 − 3x − 5 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)

Step-by-step explanation:

Given the function:

f(x) =

Find two numbers that multiply to give ac (in other words a times c), and add to give b.

What 2 numbers when multiplied give -10 and when added up -3

=> Numbers are and 2 and 5

Rewrite quadratic expression as:  

<=> (x+1)(2x-5)

Part B: x- intercepts are found when  (x+1)(2x - 5) = 0

Set factors equal to 0. we have

<=> x + 1  = 0 or 2x - 5 = 0

<=> x = -1 or x =

Part C: the lead coefficient  is a positive number which is 2, which causes the parabola to open upward. The first graph of f(x) has both "ends" of the graph pointing upward so  this can be described 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

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation:

the awnser is visionary