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
FinnZ [79.3K]
2 years ago
12

What is the factorizaion of the polynomial graphed below? assuming it has no constant factor.​

Mathematics
1 answer:
Oxana [17]2 years ago
5 0

Answer:

y = 0.96(x -√5)(x + √5).

Step-by-step explanation:

The two zeros of this polynomial are (0, 0) and (5, 0), and the vertex is (2.5, -6), all of this info readily available from the graph.

The standard equation of a vertical parabola with vertex at (h, k) is

y - k = a(x - h)^2, where the vertex is represented by (h, k).  Since we know that the vertex is (2.5, -6), the equation for the given graphed parabola is

y + 6 = a(x - 2.5)^2

Since the graph of this parabola goes through the origin, (0, 0), the following must be true if we substitute 0 for both x and y:

0 + 6 = a(0 - 2.5)^2, or 6 = a(6.25).  Thus, a = 6/6.25, or a = 0.96.

The equation of this polynomial must then be:

y + 6 = 0.96(x - 2.5)^2, which is satisfied by both (0, 0) and (5, 0).

This equation can be rewritten as

y = 0.96(x^2 - 5x + 6.25) - 6 = 0.96x^2 - 4.8x + 6 - 6, or just

y = 0.96x^2 - 4.8x.  We must factor this.  Factoring out 0.96, we get:

y = 0.96(x^2 - 5), which can be factored further:  

y = 0.96(x -√5)(x + √5).  This is the fully factored form of the polynomial.

You might be interested in
What equation is used to find the vertex form of a parabola with the vertex (h, k)?
makkiz [27]

Answer:

y=a(x-h)^{2}+h

Step-by-step explanation:

equation for vertex form of a parabola is,

y=a(x-h)^{2}+h

8 0
2 years ago
Read 2 more answers
What is the solution to the inequality 1/4(3x-6) >2(7-x +1
Vladimir79 [104]

Answer:

x>70/11

Step-by-step explanation:

5 0
2 years ago
Mr. Milleman suggested contacting a travel agent to see whether they could get a lower price. The agent found a price that was 3
Keith_Richards [23]
2075 x .30 = 622.50

2075-622.50 = $1452.50
7 0
2 years ago
Read 2 more answers
In a large population, 57 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that
ollegr [7]

Answer:0.92

Step-by-step explanation:

Given

57\% of Population is vaccinated

So, Probability of a person being vaccinated is P=0.57

and simultaneously , probability of not vaccinated is 1-P

=1-0.57=0.43

Now, Probability that atleast one of them has been vaccinated is given by

=1-P(\text{None of them is vaccinated})

=1-0.43\times 0.43\times 0.43

=1-0.0795

=0.92

7 0
3 years ago
Read 2 more answers
Help Plss simply can u show step by step ?-4(8x-4)+3x
Vikentia [17]

Answer:

-4(8x-4)+3x = -29x+16

Step-by-step explanation:

1. Simplify -4(8x-4) by using the distribution property:

<u>-4(8x) = -32x and -4(-4) = 16 so -4(8x-4) = -32x+16</u>

2. Add 3x to the remaining equation:

<u>-32x+16+3x = -29x+16 </u>

3. The answer is:

<u> -29x+16 </u>

6 0
3 years ago
Other questions:
  • Amit and Noah are the top 2 semifinalists in Moto Z. Amit scored 5/6 as many points as Noah. Who scored more points?
    15·1 answer
  • Octavia is asking about her age. My brother is 7 years older than I am. Our ages add up to 39. How old are Octavia and her broth
    10·1 answer
  • What's 25% of $130,000
    7·1 answer
  • Write the slope-intercept form of the equation that passes through the point (-2, 3) and is parallel to the line y = -6x - 9 y =
    11·1 answer
  • Help what’s this answer
    5·1 answer
  • How estimating helps you check the reasonableness of your answers
    10·1 answer
  • A box contains 14 large marbles and 11 small marbles. Each marble is either green or white. 7 of the large marbles are green, an
    8·1 answer
  • Of 10
    13·1 answer
  • URGENT!
    6·1 answer
  • Please help and show work It is super late rn
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!