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

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).