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

The person above me is correct!

Answer 2

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.