ms sue plss help
Use the function f(x) to answer the questions.
f(x) = −16x2 + 24x + 16
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)
f(x) = −16x2 + 24x + 16
is a downwards opening parabola, so it must have a maximu.
for the x-intercepts, f(x) = 0
−16x2 + 24x + 16 = 0
divide be -8
2x^2 - 3x - 2 = 0
(2x + 1)(x - 2) = 0
x = -1/2 or x = 2
the parabola cuts the x-axis at (-1/2 , 0) and (2, 0)
for y = ax^2 + bx + c , the x of the vertex is -b/(2a)
so for yours, the x of the vertex is -24/-32 = 3/4
then y = -16(3/4)^2 + 24(3/4) + 16 = 25
You could also complete the square to find the vertex ...
y = -16(x^2 -3/2 x + ....) + 16
= -16(x^2 - 3/2 x + 9/16 - 9/16) + 16
= -16( (x - 3/4)^2 - 9/16) + 16
= -16(x - 3/4)^2 + 9 + 16
= -16(x - 3/4)^2 + 25 , and got the same result
leave it up to you to put it all together
(btw, Ms Sue passed away several years ago, we all miss her)