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.

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 to draw the graph.

A)  to find the x intercepts solve for x: -
-16x^2 + 22x + 3 = 0
-(16x^2 -22x - 3) = 0
-(8x + 1)(2x -  3)   = 0
so x = -1/8 and 3/2   these are the x intercepts

b because the coefficient of x^2 is negative vertex will be a maximum
the x coordinate of the vetrex = -b/2a = -22/(2*-16) = =   11/16 or 0.6875
to find the y coordinate plug x = 0.6875 into -16x^2 + 22x + 3.

c to graph the function   mark off the 3 points: - vertex and the 2 x intercepts .   the curve will be symmetrical about the vertical line x = 0.6875 and will peak at the vertex and pass through the 2 x intercepts