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
lora16 [44]
3 years ago
15

Find the vertex of the graph of the function.

Mathematics
1 answer:
lapo4ka [179]3 years ago
3 0

Answer: The correct options are  (1) (5,10), (2) (3,-3), (3) x = -1, (4) y=(x+2)^2+3, (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

f(x)=a(x-h)^2+k        .....(1)

Where,  (h,k) is the vertex of the parabola.

(1)

The given equation is,

f(x)=(x-5)^2+10

Comparing this equation with equation (1),we get,

h=5 and k=10

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

f(x)=3x^2-18x+24

f(x)=3(x^2-6x)+24

To make perfect square add (\frac{b}{2a})^2, i.e., 9. Since there is factor 3 outside the parentheses, so subtract three times of 9.

f(x)=3(x^2-6x+9)+24-3\times 9

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

Comparing this equation with equation (1),we get,

h=3 and k=-3

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

f(x)=4x^2+8x+7

f(x)=4(x^2+2x)+7

To make perfect square add (\frac{b}{2a})^2, i.e., 1. Since there is factor 4 outside the parentheses, so subtract three times of 1.

f(x)=4(x^2+2x+1)+7-4

f(x)=4(x+1)^2+3

Comparing this equation with equation (1),we get,

h=-1 and k=3

The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.

(4)

The given equation is,

y=x^2+4x+7

To make perfect square add (\frac{b}{2a})^2, i.e., 2^2.

f(x)=x^2+4x+4+7-4

f(x)=x^2+4x+4+7-4

f(x)=(x+2)^2+3

Therefore, the correct option is  4.

(5)

The given equation is,

h=-16t^2+672t

It can be written as,

h=-16(t^2-42t)

It is a downward parabola. so the maximum height of the function is on its vertex.

The x coordinate of the vertex is,

x=\frac{b}{2a}

x=\frac{42}{2}

x=21

Therefore,  after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

f(x)=3x^3-12x^2-15x

f(x)=3x(x^2-4x-5)

Use factoring method to find the factors of the equation.

f(x)=3x(x^2-5x+x-5)

f(x)=3x(x(x-5)+1(x-5))

f(x)=3x(x-5)(x+1)

Equate each factor equal to 0.

x=0,-1,5

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

You might be interested in
What is 15456415 times 45415
masha68 [24]

Answer: 701953087225 is the answer

4 0
3 years ago
A wildlife audit was recently conducted in Port Augusta, the results of which were as follows: Amphibians Insects Fish Reptiles
r-ruslan [8.4K]

Answer:

The relative frequency of mammals in the survey is 30%.

Step-by-step explanation:

Relative frequency is the ratio of the occurrence of a singular event and the total number of outcome

Amphibians  Insects  Fish  Reptiles  Birds  Mammals

12                 30          9          25        22        42

Relative frequency = = \frac{\text{ (number of trials that are successful)}}{\text{(total number of trials)}}

Total number of wildlife animals  = 12+ 30 +9 +25+22+42 = 140

Now the relative frequency of mammals in the survey = \frac{\text{total number of mammals}}{\text{ Total number of animals}}

the relative frequency of mammals in the survey =\frac{42}{140} = 0.3

Converting into percentage , we get

=0.3 \times 100

= 30 %

5 0
3 years ago
What is seven times the quotient of five and seven?( help fill in the blanks too plz )
MrRa [10]

Answer:

7÷5

1.4×5

Solution

7÷5=1.4

1.4×5=7

3 0
3 years ago
a pair of basketball shoes was originally priced at $80, but was marked up 37.5%. what was the retail price of the shoes
Galina-37 [17]
37.5% of $80 = $30
Since it is marked up, you add $30 to the current price. 
$80 + $30 = $110.
5 0
3 years ago
HELP FIRST GET BRAINLLEST Which of the statements below are true? Select all that apply. A) Tom's friends are taller than Sam's
larisa [96]

Answer:

B and C are true

Step-by-step explanation:

hope this helps :)

8 0
3 years ago
Read 2 more answers
Other questions:
  • Your family gives you $5,000 as a college graduation present. You are about to start paying off $50,000 in student loans at a 4
    11·1 answer
  • Solve, explain why the algorithm works<br> 3892<br> -2567
    13·1 answer
  • What is the answer to 8(c-5)
    8·2 answers
  • The area and perimeter of parallelogram
    15·1 answer
  • 15 POINTS!!!!!
    15·2 answers
  • Which graph shows the inequality b≤-7
    5·1 answer
  • If 2 is equal to 156°, what is the measure of 3?
    13·1 answer
  • Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much o
    13·1 answer
  • 4(1-x)+2x=-3(x+1 solve for x
    7·1 answer
  • Julio invest $15,000 in a savings account that pays 1.5% simple interest. How much will be in the
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!