Use the function f(x) = -16^2 + 22x + 3

Question

Part A: complete factor f(x)

part b: what are the c-intercepts of the graph ? Show work

part c: describe the end behavior of the graph of f(x)

part d: what are the steps you would use to graph f(x)? Justify that can use the answers to obtain in part B and C to draw the graph

Answer 1

-16x^2 +22x + 3 = (8x+1)(-2x+3)

x intercepts are when -16x^2+22x + 3 = 0

when (8x+1)(-2x+3) = 0

or when 8x+1 = 0 and -2x+3 = 0

x=-1/8 x = 3/2

x and c are close on the keyboard, so it looks like a typo to ask for c intercepts.

as x gets very large or very small, f(x) approaches negative infinity

plot the 2 x intercepts (-1/8,0) and (3/2, 0) the line of symmetry is x = to the midpoint or (-1/8+3/2)/2 = (-1/8+12/8)/2 = 11/16, x=11/16 is the line of symmetry. 11/16 is also the x coordinate of the vertex or the point that is the maximum. It's a downward opening parabola

-16x^2 +22x + 3

-16(11/16) + 22(11/16) +3 = -11 + 121/8 + 3 = (121+24-88)/8 = 233/8 = about 29 1/8

vertex and maximum point is (11/16, 29 1/8) = (0.6875, 29.125)= about (2/3,30)

y intercept = (0,3) there's another point same distance to the other line of symmetry x=11/16. 3=11/16 = 2 5/16. add 2 5/16 to 3 to get 5 5/16. That's another point on the parabolic curve: (0, 5 5/16) or (0, 5.3125) = about (0,5 1/3)

plot the x intercepts, the y intercept and the vertex, draw a symmetrical parabolic curve through the 4 points