MATHEMATICS HIGH SCHOOL

Which of the following equations is of a parabola with a vertex at (0, -3)?y = (x - 3)^2
y = (x + 3)^2
y = x^2 - 3
y = x^2 + 3

Answers

Answer 1
Answer:

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

We need a parabola with a vertex at (0,-3)

If we select the equation:

y = x^2 - 3

When we put x = 0, we get

y=0-3\n\ny=-3

And similarly, when we put y = -3, we get

-3=x^2-3\n\n0=x^2\n\nx=0

Hence, third option is correct.
Answer 2
Answer: The\ vertx\ form:y=a(x-h)^2+k\nwhere\ the\ coordinates\ of\ vertex\ are\ (h;\ k)\n\n-------------------------\n\nvertex:(0;-3)\n\ny=a(x-0)^2+(-3)=ax^2-3\n\nif\ a=1\ then\ y=x^2-3\leftarrow answer

Related Questions

Use the rules of exponents to evaluate or simplify. Write without negative exponents.(-243)^3/5
Ok what next helppp i need 2
2+5*___=33Figure out the blank.You can use exponents
Identify the slope and y-intercept for eachUse appropriate values for the x-axis and y-axis and label each axis (see graphs above).Graph the y-intercept.Show the lines that indicate the use of slope to graph two more points (as in the quick practice and lesson).Draw the line representing the graph of the equation (as above).Save as a file and submit it.Problems:John began his job making $20 the first day. After that he was paid $6.00 per hour. Y = 6x + 20.A membership to Movie Night Movie Club costs $10 plus $2 per movie. Y = 2x +10.You start out with $20 and then spend money in a store where every item is $3. Y = -3x + 20.Your weight-lifting class cost you a $10 fee up front and $5 per class after. Y = 5x + 10.You join a paperback book club for $6, and then spend $3 per book. Y = 3x + 6.
How do you factor 8y^3+316

Arrange the circles (represented by their equations in general form) in ascending order of their radius lengths.x2 + y2 − 2x + 2y − 1 = 0
x2 + y2 − 4x + 4y − 10 = 0
x2 + y2 − 8x − 6y − 20 = 0
4x2 + 4y2 + 16x + 24y − 40 = 0
5x2 + 5y2 − 20x + 30y + 40 = 0
2x2 + 2y2 − 28x − 32y − 8 = 0
x2 + y2 + 12x − 2y − 9 = 0

Answers

The correct answer is:

x²+y²-2x+2y-1 = 0;
x²+y²-4x+4y-10 = 0;
5x²+5y²-20x+30y+40 = 0;
x²+y²-8x-6y-20 = 0;
x²+y²+12x-2y-9 = 0;
4x²+4y²+16x+24y-40 = 0; and 
2x²+2y²-28x-32y-8 = 0

Explanation:

For each of these, we want to write the equation in the form
(x+h)²+(y+k)² = r².

To do this, we evaluate the terms 2hx and 2ky in each equation.  We will take half of this; this will tell us what h and k are for each equation.

For the first equation:
2hx = -2x and 2ky = 2y.

Half of -2x = -1x and half of 2y = 1y; this means h = -1 and k = 1:
(x-1)² + (y+1)² + ___ - 1 = 0

When we multiply (x-1)², we get
x²-2x+1.
When we multiply (y+1)², we get
y²+2y+1.

This gives us 1+1 = 2 for the constant.  We know we must add something to 2 to get -1; 2 + ___ = -1; the missing term is -3.  Add that to each side (to have r² on the right side of the equals) and we have
(x-1)² + (y+1)² = 3
This means that r² = 3, and r = √3 = 1.732.

For the second equation, 2hx = -4x and 2ky = 4y; this means h = -4/2 = -2 and k = 4/2 = 2.  This gives us
(x-2)² + (y+2)² -10 + ___ = 0.

Multiplying (x-2)² gives us
x²-4x+4.
Multiplying (y+2)² gives us
y²+4x+4.
This gives us 4+4= 8 for our constant so far.

We know 8 + ___ = -10; this means the missing term is -18.  Add this to each side of the equation to have
(x-2)²+(y+2)² = 18; r² = 18; r = √18 = 3√2 = 4.243.

For the third equation, 2hx = -8x and 2ky = -6y.  This means h = -8/2 = -4 and k = -6/2 = -3.  This gives us:
(x-4)²+(y-3)²-20 = 0

Multiplying (x-4)² gives us
x²-8x+16.
Multiplying (y-3)² gives us
y²-6y+9.

This gives us 16+9 = 25 for the constant.  We know that 25+___ = -20; the missing term is -45.  Add this to each side for r², and we have that 
r²=45; r = √45 = 3√5 = 6.708.

For the next equation, we factor 4 out of the entire equation:
4(x²+y²+4x+6y-10)=0.
This means 2hx = 4x and 2ky = 6y; this gives us h = 4/2 = 2 and k = 6/2 = 3.  This gives us
4((x+2)²+(y+3)² - 10) = 0.

Multiplying (x+2)² gives us
x²+4x+4.
Multiplying (y+3)² gives us
y²+6y+9.

This gives us a constant of 4+9 = 13.  We know 13+__ = -10; this missing value is -23.  Since we had factored out a 4, that means we have 4(-23) = -92.  Adding this to each side for r², we have
r²=92; r = √92 = 2√23 = 9.59.

For the next equation, we factor out a 5 first:
5(x²+y²-4x+6y+8) = 0.  This means that 2hx = -4x and 2ky = 6y; this gives us h = -4/2 = -2 and k = 6/2 = 3:

5((x-2)²+(y+3)²+8) = 0.

Multiplying (x-2)² gives us
x²-4x+4.
Multiplying (y+3)² gives us
y²+6y+9.

This gives us a constant of 4+9 = 13.  We know that 13+__ = 8; the missing value is -5.  Since we factored a 5 out, we have 5(-5) = -25.  Adding this to each side for r² gives us
r²=25; r = √25 = 5.

For the next equation, we first factor a 2 out:
2(x²+y²-14x-16y-4) = 0.  This means 2hx = -14x and 2ky = -16y; this gives us h = -14/2 = -7 and k = -16/2 = -8:

2((x-7)²+(y-8)²-4) = 0.

Multiplying (x-7)² gives us
x²-14x+49.
Multiplying (y-8)² gives us
y²-16x+64.

This gives us a constant of 49+64=113.  We know that 113+__ = -4; the missing value is -117.  Since we first factored out a 2, this gives us 2(-117) = -234.  Adding this to each side for r² gives us
r²=234; r = √234 = 3√26 = 15.297.

For the last equation, 2hx = 12x and 2ky = -2; this means h = 12/2 = 6 and k = -2/2 = -1:
(x+6)²+(y-1)²-9 = 0

Multiplying (x+6)² gives us
x²+12x+36.
Multiplying (y-1)² gives us
y²-2y+1.

This gives us a constant of 36+1 = 37.  We know that 37+__ = -9; the missing value is -46.  Adding this to each side for r² gives us
r² = 46; r=√46 = 6.78.
Find the radius of each equation:

1.
 x^2 + y^2-2x+2y-1 = 0, \n x^2-2x+1-1 + y^2+2y+1-1-1 = 0, \n (x-1)^2+(y+1)^2=3, then r_1= √(3).

2. 
x^2 + y^2-4x + 4y- 10 = 0, \n x^2 -4x+4-4+ y^2 + 4y+4-4- 10 = 0, \n (x-2)^2+(y+2)^2=18, then r_2= √(18)=3 √(2).

3.
 x^2 + y^2-8x- 6y- 20 = 0, \n x^2-8x+16-16+ y^2- 6y+9-9- 20 = 0, \n (x-4)^2+(y-3)^2=45, then r_3= √(45) =3 √(5).


4.
4x^2 + 4y^2+16x+24y- 40 = 0, \n 4x^2+16x+16-16+ 4y^2+24y+36-36- 40 = 0, \n 4(x+2)^2+4(y+3)^2=92,\n (x+2)^2+(y+3)^2=23, then r_4= √(23).

5.
 5x^2 + 5y^2-20x+30y+ 40 = 0, \n 5x^2-20x+20-20+ 5y^2+30y+45-45- 40 = 0, \n 5(x-2)^2+5(y+3)^2=105,\n (x-2)^2+(y+3)^2=21, then r_5= √(21).

6.
 2x^2 + 2y^2-28x-32y- 8= 0, \n 2x^2-28x+98-98+ 2y^2-32y+128-128- 8= 0, \n 2(x-7)^2+2(y-8)^2=234,\n (x+2)^2+(y+3)^2=117, then r_6= √(117)=3√(13).

7. 
x^2 + y^2+12x-2y-9 = 0, \n x^2+12x+36-36+ y^2-2y+1-1- 9 = 0, \n (x+6)^2+(y-1)^2=46, then r_7= √(46).

Hence
r_1= √(3), r_2=3 √(2), r_3=3 √(5), r_4= √(23), r_5= √(21), r_6= 3√(13), r_7= √(46) and r_1\ \textless \ r_2\ \textless \ r_5\ \textless \ r_4\ \textless \ r_3\ \textless \ r_7\ \textless \ r_6.

The area of a rectangular wall of a barn is 108 square feet. Its length is 12 feet longer than the width. Find the length and width of the wall of the barn.

Answers

Area = Width x Length
Area = 108
Square root of 108 = 10.4

108/ 9 = 12      ...12 is not 12 larger than 9
108/ 6 = 18      ...18 is 12 larger than 6

108 = 6 x 18

Width = 6
Length = 18

Final answer:

To find the length and width of the wall of the barn, set up an equation using the given information. Solve the equation by factoring, and find the values of x and x + 12, which will be the width and length of the wall, respectively. The width of the wall is 6 feet, and the length is 18 feet.

Explanation:

To find the length and width of the wall of the barn, we can use algebra. Let's say the width of the wall is x. According to the problem, the length is 12 feet longer than the width, so the length is x + 12.

The area of a rectangle is found by multiplying the length by the width, so we can set up the equation

x(x + 12) = 108.

Solving this equation will give us the values of x and x + 12, which will be the width and length of the wall, respectively.

The equation is x(x + 12) = 108.

Expanding the equation gives x^2 + 12x = 108.

Rearranging the equation to bring everything to one side gives

x^2 + 12x - 108 = 0.

Factoring the quadratic equation gives (x + 18)(x - 6) = 0.

Setting each factor equal to zero gives x = -18 or x = 6.

Since we can't have a negative width, the width of the wall is 6 feet.

Therefore, the length of the wall is x + 12 = 6 + 12 = 18 feet.

Learn more about Solving equations to find length and width of a rectangular wall here:

brainly.com/question/34778989

#SPJ3

What is the equivalent function in standard form of y=(x+5)(x+1)

Answers

FOIL (x+5) and (x+1)

x^2+x+5x+5
(Combine like terms)

y= x^2+6x+5

An artist wants to make alabaster pyramids using a block of alabaster with a volume of 576 cubic inches. She plans to make each pyramid with a square base area of 3 square inches and a height of 4 inches. At most, how many pyramids can the artist make from the block of alabaster?

Answers

pyramid
volume=base area times height times 1/3
or
length times widht times height times 1/3
base area=3
3 times height iems 1/3
height=4
3 times 3 times 1/3=4 times 1/3 times 3=4 times 1
each pyramide=4 in volume
so
x pyramids =alabaster volume
divide by pyramids
x=alabaster/pyrimds
alabaster=576
pyramids=4
divide
576/4=144
the artis can make 144 pyramids

Which of the following is equivalent tothe expression below?
(5x +6y- 3z) (3x- 8y+ z)
A. 8x- 14y- 4z
B. 8x- 2y -2z
C. 8x- 14y- 2z
D.8x -2y -3z

Answers

I believe the answer is B.
5+3=8
therefore being 8x
6-8=-2
therefore being -2y
-3+1=-2
there for being -2z
8x-2y-2z

hope this helps

If you multiply a negative number with a positive, what will the number be?

Answers

Answer: Negative

Step-by-step explanation:

Look at it this way

+ - +

- + -

+ - +

No matter what way you do it, if you make a "tic-tac-toe" line in any direction, it'll make the answer

Answer:

it will be negative

Step-by-step explanation:

like if i multiplied -6 by positive 5 the answer is negative 30
Other Questions
What is another way to write the ratio 3 to 10
Do you expect δhsoln to be a large positive number, a large negative number, or close to zero? do you expect to be a large positive number, a large negative number, or close to zero? δhsoln is a large positive number. δhsoln is a large negative number. δhsoln is close to zero.
Identify the explanatory and response variables in the following situation:There is a strong negative correlation between latitude above the equator and average temperature on December 21. A: Explanatory: Latitude Response: Daylight hours B. Explanatory: Latitude Response: Average temperature C. Explanatory: Daylight hours Response: Latitude D. Explanatory: Time of year Response: Daylight hours
What is the Turing point of f(x)=x^2-2x+8