Question

Use the function f(x) = −16x2 + 24x + 16 to answer the questions.

Part A: Completely factor f(x). (2 points)

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

Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)

Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)

Answer 1

Answer:

answer is part B.

Step-by-step explanation:

plz mark me as brainliest

Answer 2

Answer:

The answer is

Step-by-step explanation:

Given :

f(x) = $-16x^{2} + 24x + 16$

f'(x) = -32x + 24

Function f(x) is a quadratic function.

1. Completely factor f(x).

For the given function f(x) = $-16x^{2} + 24x + 16$,

24x can be split as -32x + 8x

∴ f(x) becomes

f(x) = $-16x^{2} -32x + 8x + 16 = 0$

f(x) = -16x(x + 2) +8(x + 2) = 0

f(x) = (x + 2)(-16x + 8) = 0

∴ For f(x),

x = -2 or x = $\frac{-8}{-16} = \frac{1}{2}$

∴ For f(x),

x = -2 or $\frac{1}{2}$

2. X-intercepts of the graph of f(x)?

For a graph intercepts are the points at which the graph of a function meets or crosses x axis and y axis.

For f(x) = $-16x^{2} + 24x + 16$,

x intercepts are none other than the factors of the graph

∵ x = -2 or $\frac{1}{2}$

∴ For f(x) = $-16x^{2} + 24x + 16$,

x intercepts are x = -2 and x = $\frac{1}{2}$.

3. End behavior of the graph f(x)

• For the given function f(x) = $-16x^{2} + 24x + 16$, f(x) is a quadratic equation.
• The graph of a quadratic equation is always parabolic in nature.
• Therefore, graph for function f(x) = $-16x^{2} + 24x + 16$,  will be parabolic.
• These graph will intercept with x axis at points x = -2 and x = $\frac{1}{2}$.

4. Steps you would use to graph f(x)? Justify

• To draw a graph of given equation one need to first find its x intercepts and y intercepts.
• One also need to find first derivative of the given equation, and equate it to zero to find the pick point.
• With the help of these values one can find/draw the graph for any equation given.

#SPJ2