Question

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) My answers: PART A: (-1/8, 0) & (3/2, 0) PART B: (11/8,3) vertex = maximum. PART C: must have the vertex, axis of symmetry, and zeros (or x-intercepts)

Answer 1

Step-by-step explanation:

f(x) = -16x² + 22x + 3

Factor:

f(x) = (8x + 1) (-2x + 3)

The x-intercepts are (-1/8, 0) and (3/2, 0).

The leading coefficient is negative, so the parabola points down.  Therefore, the vertex is a maximum.  The x-coordinate is halfway between the x-intercepts.

x = (-1/8 + 3/2) / 2

x = 11/16

f(11/16) = 169/16

So the vertex is at:

(11/16, 169/16)

Graph the x-intercepts and the vertex, then draw a curve through the 3 points.