1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gtnhenbr [62]
3 years ago
13

SHOW ALL WORK!!! Use the function f(x) = −16x2 + 24x + 16 to answer the questions. Part A: Completely factor f(x). (2 points) Pa

rt 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)

Mathematics
1 answer:
Zolol [24]3 years ago
6 0

Answer:

see below

Step-by-step explanation:

f(x) = −16x^2 + 24x + 16

Factor out -8

f(x) = -8( 2x^2-3x-2)

Factor

f(x) = -8 (x-2) ( 2 x+1)

Set equal to zero to find the x intercepts

0 =  -8 (x-2) ( 2 x+1)

Using the zero product property

x-2 =0   2x+1 =0

x=2     2x=-1

x=2   x = -1/2

The x intercepts are

(2,0)  and (-1/2,0)

The end behavior

Let x = -∞

f(x) = −16( -∞)^2 + 24( -∞) + 16

      The squared term dominates

     =  −16( -∞)^2 =   −16( ∞) =   −( ∞)

It goes to  -∞ as x goes to ( -∞)    

Let x = ∞

f(x) = −16( ∞)^2 + 24( ∞) + 16

      The squared term dominates

     =  −16( ∞)^2 =    −16( ∞) =   −( ∞)

It goes to  -∞ as x goes to ( ∞)    

We need the vertex, the zeros and the end behavior to graph the parabola

The vertex is  1/2 way between the zeros

(-1/2+2) /2 = 3/4

f(3/4) =  -8 (3/4-2) ( 2 *3/4+1) = 25

We know it opens down since the x^2 term has a negative coefficient

You might be interested in
Please need some help on this
vredina [299]
11111111111111117373646328299292922
8 0
3 years ago
A scale drawing of jimmy's living room is shown below width =4cm length =6cm
Semenov [28]
Do you need the area of the floor plan? If so here you go:

6*4 = 24, so 24 cm.
7 0
3 years ago
3in x 8in x 5in = ?<br><br> using cubic squares!!
KonstantinChe [14]

Answer:

120

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What does the phrase between 7.2 and 7.6 inclusive mean
Naddik [55]
It means that if u subtract idk lol
6 0
3 years ago
Tlus<br> Reduce answers to their lowest<br> terms and mixed forms.<br> 5<br> +<br> 7
MissTica

Answer:

41/28

Step-by-step explanation:

mixed form is 13/28*1

follow me please.

5 0
3 years ago
Other questions:
  • A small auditorium has 10 rows of seats. There are 12 seats in the row and 16 seats in the second row the number of seats in a r
    6·1 answer
  • X^2-25=0 Using factoring method
    5·2 answers
  • Mr.Smith bought 5 movie tickets. The total cost was $38.75. How much did each ticket cost?
    15·2 answers
  • PLEASE HELP - Part A Find the value of x in the following figure: Part B Find the measure of ACD
    7·1 answer
  • Solve for x. 25 - 3x = -5(1 - x) - 2x
    12·2 answers
  • Any one know the answer
    10·2 answers
  • A pie can be cut into more than seven pieces by making four diameter cuts.
    12·2 answers
  • Sam computed a 95% confidence interval for μ from a specific random sample. His confidence interval was 10.1 &lt; μ &lt; 12.2. H
    8·1 answer
  • A soccer player gets 2 points for a goal and 1 point for an assist. If the combined number of goals and assists that a player ha
    7·1 answer
  • What is the value found using the linear​ approximation? ln(0.93) ≈
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!