Question

30 POINTS!!! WILL MARK BRAINLIEST IF YOU SHOW ALL YOUR WORK!!!

Use the function f(x) = 2x2 − x − 10 to answer the questions.


Part A: Completely factor f(x). Show all your work. (2 points)


Part B: What are the x-intercepts of the graph of f(x)? Show all 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)

Answer 1

Answer:

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:

2x^2-3x-5=y

(2x-5)(x+1)=y

(2x-5)(x+1)=0

2x-5=0

2x=5

x=2.5

x+1=0

x=-1

you have an even degree (2) and a positive coefficient (2)

therefore as x---> -∞, f(x)----> +∞

also, as x----> +∞, f(x)----> +∞

also notice that this is a parabola that opens upwards so both "ends" approach positive infinity

plot the x-intercepts, find the vertex using h=-b/2a and substituting this value into the equation to find k and make a table of values to graph the parabola unless you only want a rough sketch of the graph-you know the x-intercepts and you found the vertex using h=-b/2a

Mark brainliest please.