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2 years ago

Make a conjecture about why the term quadratic parent function includes the word parent.

Mathematics

1 answer:

Ne4ueva [31]2 years ago

5 0

Answer:

Quadratic pattern function is the main function that can generate infinitely many functions depending on the coefficient of X^2

Step-by-step explanation:

The reason behind the word "parent" is based on the fact that the quadratic pattern function is the main function that can generate infinitely many functions depending on the coefficient of X^2

In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions having the general form

y=ax^{2}+bx+c

the simplest function is

y=x^{2}

This is therefore the parent function of the family of quadratic equations.

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Functions f(x) and g(x) are shown: f(x) = x2 g(x) = x2 − 8x + 16 In which direction and by how many units should f(x) be shifted

denis23 [38]

Answer:

Shift right by 4

Step-by-step explanation:

Given f(x)=x^2

g(x)= x^2-8x+16

Using

Horizontal Shift theorem dealing with the question

If the graph were to be move to to the right, we must use of graph f (x-L)

Where L= 4 and

NOTE:

POSITIVE L MAKES GRAPH SHIFT RIGHT

2) NEGATIVE MAKES GRAPH SHIFT LEFT

g(x)= x^2-8x+16

If we factorize this we have

(x-4)(x-4)

Since the two terms are the same we have (x-4)^2

Then it can move by factor of 4 to the right since constant 4 can be substracted from the parents function

4 0

2 years ago

The family size bottle of sunscreen holds 121212 fluid ounces (\text{fl oz})(fl oz)left parenthesis, start text, f, l, space, o,

svlad2 [7]

I cant understand your question

4 0

2 years ago

Write an expression for the number of tiles Bruce used and an expression for the number of tiles Felicia used. Use x to represen

Basile [38]

Expression for the number of tiles Bruce used : <u>5x+2</u>

Expression for the number of tiles Felicia used : <u>5x + 5</u>

<h3>Further Explanation </h3>

One variable linear equation is an equation that has a variable and the exponent number is one.

Can be stated in the form:

$\large{\boxed{\bold{ax=b}}$

ax + b = c, where a, b, and c are constants, x is a variable

We complete the introduction for the task

Bruce retiled his kitchen. Originally, he bought three boxes of tile with the same number of tiles in each. He ran out of tile and had to go back to get three extra boxes of tile. However, he only used two tiles from the last box to finish the job.

Felicia also retiled her kitchen. She bought five boxes of tile with the same number of tiles that were in each as Bruce’s boxes. She also ran out of tile. She had to go back to the store and get an extra five tiles to finish the job.

We can translate those in to expression of One variable linear equation (x = number of tiles)

Bruce

He bought three boxes ⇒ 3x

He only used two tiles from the last box ⇒ 2x + 2

Total tiles of Bruce used : 3x+2x+2 = 5x+2

Felicia

She bought five boxes ⇒ 5x

She get an extra five tiles to finish the job. ⇒ 5 tiles

Total tiles of Felicia used : 5x+5

<h3>Learn more</h3>

linear equation

brainly.com/question/13101704

Keywords : an expression, linear equation, tiles, box,Bruce,Felicia

#LearnWithBrainly

8 0

2 years ago

Read 2 more answers

Can someone help meee???

Phoenix [80]

Answer:

Step-by-step explanation:

Couldn't really read the tables so i'd double check to make sure i'm correct

4 0

2 years ago

Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the ea

Zolol [24]

Answer:

A) The amount of gas they bought on each coast;

East Coast = 35 gallons

Mid-US = 100 gallons

West Coast = 15 gallons

B) The amount of gas they bought on each coast on the return journey;

East Coast = 37 gallons

Mid-US = 116 gallons

West Coast = 21 gallons

Step-by-step explanation:

Complete Question

Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the east coast to $3 in the mid-US, to $5 on the west coast.

(a) If they used twice as much gas in the mid-US than on either coast combined, and they spend $515 on gas to purchased 150 gallons of gas, how many gallons of gas did they buy at each price?

The answer to this question is East Coast - 35 gal, Mid-US - 100 gal, West Coast - 15 gal.

(b) On their way back they had more baggage in the car and spend $601 for 174 gallons of gas. Based on the same ratio as in Part (a), how many gallons of gas did they buy at each price? I don't know the answer to this one

Solution

Let the amount of fuel bought on the east coast = x gallons

Let the amount of fuel bought on the mid-coast = y gallons

Let the amount of fuel bought on the west coast = z gallons

a) - They used twice as much gas in the mid-US than on either coast combined

y = 2(x + z) = 2x + 2z (eqn 1)

- They spend $515 on gas to purchase 150 gallons of gas.

Total gallons purchased = x + y + z = 150

Total amount spent = 4x + 3y + 5z = 515

From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations

x + y + z = x + 2x + 2z + z = 150

3x + 3z = 150

Divide through by 3

x + z = 50 (eqn *)

4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 515

4x + 6x + 6z + 5z = 515

10x + 11z = 515 (eqn **)

x + z = 50

10x + 11z = 515

Solving the simultaneous equation,

x = 35 gallons

z = 15 gallons

y = 2x + 2z = 2(35 + 15) = 100 gallons

B) On the return journey, the ratio between x, y and z is still the same, but the total gallons and total amount spent is now different.

They used twice as much gas in the mid-US than on either coast combined

y = 2(x + z) = 2x + 2z (eqn 1)

- They spend $601 on gas to purchase 174 gallons of gas.

Total gallons purchased = x + y + z = 174

Total amount spent = 4x + 3y + 5z = 601

From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations

x + y + z = x + 2x + 2z + z = 174

3x + 3z = 174

Divide through by 3

x + z = 58 (eqn *)

4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 601

4x + 6x + 6z + 5z = 601

10x + 11z = 601 (eqn **)

x + z = 58

10x + 11z = 601

Solving the simultaneous equation,

x = 37 gallons

z = 21 gallons

y = 2x + 2z = 2(37 + 21) = 116 gallons

Hope this Helps!!!

5 0

2 years ago