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
Is 0.7142857.... a rational number? why or why not?
Andreyy89
The number 0.7142857 is definitely a rational number. This number can also be expressed as 7142857/10000000. Now we know that a rational number is a number that can be expressed as a fraction or a quotient of two integers. The denominator of the fraction can never be equal to zero. In case of the number given we can clearly see that the denominator of this fraction is not zero. The actual fraction of this number is 5/7. In this case we find that the denominator is not zero.



4 0
3 years ago
Steve washed 15 cars in 3 hours.how many cars can he wash in 7 hours?
DanielleElmas [232]
35 Cars because, if you times 3 by 5 it equals 15 which means that 1 hour equals 5 cars. So you times 7 by 5 and that will give you the amount of cars that were washed.
3 0
3 years ago
Which is correct regarding the statement: "If x is an odd integer, then the median of x, x + 2, x + 6, and x + 10 is an
nadya68 [22]

Answer:

the answer is d.the statement is always true

Step-by-step explanation:

take x as odd integer

So,

x+2=1+2=3

x+6=3+6=9

3 0
2 years ago
Zach wants to build a slanted skateboard ramp. He knows he wants the ramp to form a 15 degrees angle with the ground and be 4 fe
Fynjy0 [20]

Answer: The ramp would be 15.5 feet long.

Step-by-step explanation: Please refer to the attached diagram for details.

Angle C shows the angle to be formed by the ramp from the ground, which is 15 degrees. Also, from the ground, it’s going to be four feet tall, which is line AB. The top of the ramp is point A, which makes line AC the entire length of the ramp. Since we have a reference angle (angle C) and two sides, the opposite and the hypotenuse, we shall apply the trigonometric ratio.

SinC = opposite/hypotenuse

Sin 15 = 4/b

By cross multiplication we now have

b = 4/Sin15

b = 4/0.2588

b = 15.4599

Approximately b = 15.5

Therefore the length of the ramp would be 15.5 feet

6 0
3 years ago
Find the approximate distance between (-5, 8) and (10, -7). Round your answer to two decimal places.
nadya68 [22]
Distance formula : d = sqrt (x2 - x1)^2 + (y2 - y1)^2
(-5,8)(10,-7)

d = sqrt (10 - (-5)^2 + (-7 - 8)^2
d = sqrt (10 + 5)^2 + (- 15^2)
d = sqrt (15^2) + (-15^2)
d = sqrt 225 + 225
d = sqrt 450
d = 21.21
5 0
3 years ago
Other questions:
  • Find the value of the variable for which the value of the expression –3(2x+1) is 20 greater than the value of the expression 8x+
    8·1 answer
  • A band leader randomly selects 2 students out of 75 band members. If you and your brother are both band members, what is the pro
    11·2 answers
  • You are given a circle of radius 12. What is the segment area of an arc that is 90 degrees?
    8·1 answer
  • What is the prime factorization of 360?
    9·1 answer
  • How can you use powers and exponents to express known quantities
    11·1 answer
  • Let f(x)=-3x and g(x) = 2x-1<br> Find the following: 4g(x) - f(x)
    10·2 answers
  • Find 3 consecutive EVEN integers with a sum of 156. For your answer, just type the THIRD number. Do NOT type the first two numbe
    11·1 answer
  • Help i'll give brainlesttt
    10·2 answers
  • What is 91 divided by 0.7
    9·2 answers
  • You are building a ramp for your grandparent’s house. The ramp will replace the steps that go to their front door which is 3 fee
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!