50 POINTS Use the function f(x) to answer the questions.

f(x) = −16x2 + 22x + 3

Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)

Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)

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 to draw the graph. (5 points)

work and answers below

Draw a parabola concave down with vertex at . Since the leading coefficient of the equation is -16, the parabola should appear thinner than its parent function . Ensure that the parabola passes through the points and .

Step-by-step explanation:

Part A:

The x-intercepts of a function occur at . Therefore, let and solve for all values of :

The quadratic formula states that the real and nonreal solutions to a quadratic in standard form is equal to .

In , assign:

Therefore, the solutions to this quadratic are:

The x-intercepts are then and .

Part B:

The a-term is negative and therefore the parabola is concave down. Thus, the vertex will be the maximum of the graph. The x-coordinate of the vertex of a quadratic in standard form is equal to . Using the same variables we assigned earlier, we get:

Substitute this into the equation of the parabola to get the y-value:

Therefore, the vertex of the parabola is located at

no not all of them.

step-by-step explanation:

some of them have a square base.

6.5

step-by-step explanation:

you said it was in the question

~courtney