WILL REWARD MEDAL please help

An expression is shown below:
f(x) = -16x2 + 22x + 3

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

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. (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)

Question

WILL REWARD MEDAL please help

An expression is shown below:
f(x) = -16x2 + 22x + 3

Part A: What are the x-intercepts of the graph of the f(x)? Show your work. (2 points)

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. (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)

johnweldon1993 · Answer

$$\large f(x) = -16^2 + 22x + 3$$

A) the x-intercepts are when f(x) = 0 so we set this equation = 0 and solve for 'x'

$$\large -16x^2 + 22x + 3 = 0$$

You can do the quadratic formula for this

For part B) The vertex formula would be $$\large Vertex = -\frac{b}{2a}$$
Where 'b' and 'a' are the same as in part A

And we know it would be a MAXIMUM here because the parabola (since it is -16x^2) is like an upside down U

Part C) well you would use the 'x-intercepts' you found in A, and the vertex for the top point in B and just connect the points in a parabolic form