Question

ALL I NEED HELP WITH IS WITH PART D, HOW DO I GET THAT

Use the function f(x) = −16x^2 + 22x + 3 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)

Answer 1

Step-by-step explanation:

Step 1:  Factor the equation

$f(x) = -16x^{2} + 22x + 3\\f(x) = -(8x + 1)(2x - 3)$

Step 2:  Find the x-intercepts of the graph of f(x)

$-8x - 1 + 1 = 0 + 1\\-8x / -8 = 1 / -8\\x = -1/8$

$2x - 3 + 3 = 0 + 3\\2x / 2 = 3 / 2\\x = 3/2$

Step 3:  Describe the end behavior of the graph of f(x)

Since the function is to the power of 2, that means that it is a parabola.  And since the leading coefficient is negative, means that the arrows will be pointing down therefore, the end behavior of this graph is as x goes to infinity, f(x) goes to negative infinity and as x goes to negative infinity, f(x) goes to negative infinity.

Step 4:  What are the steps you would use to graph f(x)

The first step that I would do is factor the equation.  Then I would find the x-intercepts of the graph and plot them on the graph.  I would then plug in 0 for all of the x values to get the y intercept.  After doing that I would get the vertex using the vertex formula plotting it on the graph.  Finally, I would connect all of the dots together to form the graph of the equation.

Answer 2

Answer:

The person above me is correct!