F(x) = -16x^2 + 22x + 3

Question

Part A: What are the x-intercepts of the graph of f(x)? Show your work.

Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.

Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and part B

Answer 1

Hi Rose!

Here are some things to think about to help you get started on this problem.

Part A: You can either factor the equation or use the quadratic formula to solve for the zeros of this function. For this equation, it would likely be easier to use the quadratic formula.

Part B: Does the function open up or down? If the leading coefficient is negative, then the function opens down. If the leading coefficient is positive, then the function opens up. How does the direction of opening help you determine whether there is a maximum or minimum? The x-value of the vertex is given by x=-b/(2a). Use this x-value to find the y-value of the vertex.

Part C: Use your answers from Part A & Part B to answer this question.

Feel free to reach out if you need further help.