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oksano4ka [1.4K]
3 years ago
6

If you horizontally stretch the linear parent function, f(x) = x, by a factor of 3, what is the equation of the new function?

Mathematics
1 answer:
vekshin13 years ago
3 0
The correct answer is C
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Express each of the following quadratic functions in the form of f(x) = a (x - h)²+ k.Then,state the minimum or maximum value,ax
Ivan

Given:

The function is:

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

To find:

Express the quadratic equation in the form of f(x)=a(x-h)^2+k, then state the minimum or maximum value,axis of symmetry and minimum or maximum point.

Solution:

The vertex form of a quadratic function is:

f(x)=a(x-h)^2+k              ...(i)

Where, a is a constant, (h,k) is the vertex and x=h is the axis of symmetry.

We have,

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

It can be written as:

f(x)=-2\left(x^2-3.5x\right)+4

Adding and subtracting square of half of coefficient of x inside the parenthesis, we get

f(x)=-2\left(x^2-3.5x+(\dfrac{3.5}{2})^2-(\dfrac{3.5}{2})^2\right)+4

f(x)=-2\left(x^2-3.5x+(1.75)^2\right)-2\left(-(1.75)^2\right)+4

f(x)=-2\left(x-1.75\right)^2+2(3.0625)+4

f(x)=-2\left(x-1.75\right)^2+6.125+4

f(x)=-2\left(x-1.75\right)^2+10.125                ...(ii)

On comparing (i) and (ii), we get

a=-2,h=1.75,k=10.125

Here, a is negative, the given function represents a downward parabola and its vertex is the point of maxima.

Maximum value = 10.125

Axis of symmetry : x=1.75

Maximum point = (1.75,10.125)

Therefore, the vertex form of the given function is f(x)=-2\left(x-1.75\right)^2+10.125, the maximum value is 10.125, the axis of symmetry is x=1.75 and the maximum point is (1.75,10.125).

8 0
3 years ago
X=4, y= -7, z=9 solve: -2x-3y+z
vesna_86 [32]

Answer:

22

Step-by-step explanation:

To solve this we can plug the values in.

-2x-3y+z

-2(4)-3(-7)+(9)

Simplify.

-8+21+9

Add.

22

8 0
3 years ago
Evaluate 5m2 for m=4
jolli1 [7]
If the question is 5m^2 the answer is 80. And if the question is 5m2 then it is 40
4 0
3 years ago
Read 2 more answers
A school has 17 tables in the cafeteria. Each table seats 12 students. What is the
Scorpion4ik [409]

Answer: 204 students

Step-by-step explanation: To find  out the greatest number of students that can fit at the 17 tables in the school cafeteria, we simply need to multiply the number of students that can fit at each table by the number of tables.

12 students can fit at 1 table and there are 17 tables.

So we have (12)(17) which is 204.

So the greatest number of students that can be seated din the cafeteria is 204 students.

8 0
3 years ago
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Ms. Franco earned $709.54 in net pay for working 25 hours. She paid $87.45 in federal and state taxes, and $38.45 in FICA taxes.
GenaCL600 [577]

Answer:

The hourly wage of Ms. Franco is $28.38 .

Option (B) is correct .

Step-by-step explanation:

As given

Ms. Franco earned $709.54 in net pay for working 25 hours.

Thus

Hourly\ wage\ of\ Ms. France = \frac{Total\ wage}{Total\ number\ of\ hours}

Putting values in the above

Hourly\ wage\ of\ Ms. France = \frac{709.54}{25}

Hourly wage = $ 28.38

Therefore the hourly wage of Ms. Franco is $28.38 .

Option (B) is correct .

7 0
3 years ago
Read 2 more answers
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