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erastova [34]
3 years ago
9

Use the method of completing the square to write the equation of the given parabola in this form:

Mathematics
2 answers:
siniylev [52]3 years ago
6 0
Formula is y = a(x-h)^2 + k

Where h is 1 and k is 1

f (x) = a(x-1)^2 + 1

-3 = a(0-1)^2 + 1

-3 = a(-1)^2 + 1

-3 = a(1) + 1

-3 - 1 = a

-4 = a

a = -4

A must be equal to -4

y = -4(x-1)^2 + 1

0 = -4(x-1)^2 + 1

4(x^2 - 2x + 1) - 1 = 0

4x^2 - 8x + 4 - 1 = 0

4x^2 - 8x + 3 = 0

4x^2 - 8x = -3

Divide fpr 4 each term of the equation....x^2 - 2x = -3/4

We must factor the perfect square ax^2 + bx + c which we don't have. We must follow the rule (b/2)^2 where b is -2....(-2/2)^2 = (-1)^2 = 1 and we add up that to both sides

x^2 - 2x + 1 = -3/4 + 1

x^2 - 2x + 1 = 1/4

(x-1)^2 = 1/4

square root both sides x-1 = (+/-) 1/2

x1 = +1/2 + 1 = 3/2

x2 = -1/2 + 1 = 1/2

x-intercepts are 1/2 and 3/2, in form (3/2,0); (1/2,0)
kobusy [5.1K]3 years ago
6 0

So in this question we are trying to find the two x - intercepts.

y = a(x-h)^2 + k  
is the formula


f (x) = a(x-1)^2 + 1

-3 = a(-1)^2 + 1


-3 = a(1) + 1

-3 - 1 = a

a = -4

So <span>a is -4.

</span>y = -4(x-1)^2 + 1

4(x^2 - 2x + 1) - 1 = 0

4x^2 - 8x + 4 - 1 = 0

4x^2 - 8x + 3 = 0

4x^2 - 8x = -3

So our standard form is:
4x^2 - 8x = -3&#10;

( \frac{3}{2} ,0)

and

(\frac{1}{2} ,0)

are you x - intercepts.

Also, in Plato put a comma in-between the intercepts

(x_{1} y_{1}),( x_{2} , y_{2} )<u />

Hope I've helped!
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3 years ago
Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y 2x3y4 xy3?.
ki77a [65]

The degree of the sum and difference of the polynomials are 6 and 7 respectively.

given polynomials are:

3x^5-2x^3y^4-7xy^3

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the sum of polynomials = -5x^5y-6xy^3

the difference of polynomials = 11x^5y-4x^3y^4-8xy^3

<h3>what is the degree of a polynomial?</h3>

A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.

degree of sum = monomial with highest power = 5+1=6

degree of difference = monomial with highest power = 3+4 = 7

therefore, the degree of the sum and difference of the polynomials are 6 and 7 respectively.

to get more about polynomials refer to:

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4 0
1 year ago
Please help me with this 100 points
Serjik [45]

Answer:

2m + 153.5

Step-by-step explanation:

Hey there

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5 0
3 years ago
Read 2 more answers
Suppose RS is conjurated to MN. For each of the set of lengths, solve for X, and find the length of each segment.
NeX [460]

If RS is congruent to MN then the value of x in all the parts are 6,4, and 10.

Given RS is congruent to MN.

We are required to find the value of x if RS is congruent to MN.

Congruent lines are those lines whose lengths are equal to each other.

1) RS=x+10, MN=2x+4.

Because the congruent lines have equal lengths so , RS=MN.

x+10=2x+4

x-2x=4-10

-x=-6

x=6

2) RS=3x-2, MN=x+6

Because the length of lines are equal,so RS=MN.

3x-2=x+6

3x-x=6+2

2x=8

x=4

3) RS=5x-10, MN=2x+20

The lengths are equal so RS=MN.

5x-10=2x+20

5x-2x=20+10

3x=30

x=10

Hence if RS is congruent to MN then the value of x in all the parts are 6,4, and 10.

Learn more about congruent lines at brainly.com/question/28220245

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3 0
1 year ago
Someone help me please
AlladinOne [14]
To find the equation of a line, you need to find the slope and y-intercept by using the slope formula and point slope formula. 

First, let's find the slope. 11 + 5/9 - 1 = 16/8 = 2. Therefore, the slope is 2.

Then, plug it into the point slope formula. 
y + 5 = 2(x - 1). 
Distribute: y + 5 = 2x - 2

Subtract 5 on both sides: y = 2x - 7. 

Your final equation, that you need to plug into your answer, is y = 2x - 7.

Hope this helps!! If you need further assistance, message me or comment under this post!
7 0
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