Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2?g(x) = –9(x2 + 2x + 1) – 7
g(x) = 4(x2 – 6x + 9) + 1
g(x) = –3(x2 – 8x + 16) – 6
g(x) = 8(x2 – 6x + 9) – 5

Answers

Answer 1

Answer:

Answer:

g(x) = 8(x2 – 6x + 9) – 5

Step-by-step explanation:

A function with a form (x - a)^2 - b where a and b are some constants are a transformation to the right and down from the parent function, f(x) = x^2. Then, option:

g(x) = 4(x2 – 6x + 9) + 1 = 4(x - 3)^2 + 1

is discarded

The vertex form of a quadratic equation is f(x) = c*(x - h)^2 + k, where c, h and k are all constant, and point (h,k) is the vertex of the quadratic function. If c > 0, then the vertex is a minimum and if c < 0 then the vertex is a maximum. Therefore, options:

g(x) = –9(x2 + 2x + 1) – 7 = -9(x + 1)^2 - 7

g(x) = –3(x2 – 8x + 16) – 6 = -3(x - 4)^2 - 6

are dicarded

In consequence, the correct option is:

g(x) = 8(x2 – 6x + 9) – 5 = 8(x - 3)^2 - 5

Answer 2

Answer:

Answer:

The last choice is the one you want

Step-by-step explanation:

First of all, a parabola has a minimum value if it is a positive parabola, one that opens upward. The first and the third parabolas are negative so they open upside down. That leaves us with choices 2 and 4. We find the side to side and up or down movement by finishing the completion of the square that has already been started for us. Do this by factoring what's inside the parenthesis into a perfect square binomial.

The second one factored becomes:

$g(x)=4(x-3)^2+1$

which reflects a shift to the right 3 and up 1. Not what we are asked to find.

The fourth one factored becomes:

$g(x)=8(x-3)^2-5$

which reflects a shift to the right 3 and down 5. That's what we want!

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Answer correct for brainliest and also get a thanks !:-) answer A and B!
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The mass of an electron is approximately 9 × 10-28 grams, while the mass of a neutron is approximately 2 × 10-24 grams. Which of the following is true?The mass of a neutron is approximately 2,000 times the mass of an electron. The mass of a neutron is approximately 10,000 times the mass of an electron. The mass of a neutron is approximately 20,000 times the mass of an electron. The mass of a neutron is approximately 1,000 times the mass of an electron.
Solve for x and y simultaneouslyx+3y=5xy+y² =3

Given that the measure of ∠x is 60°, and the measure of ∠y is 90°, find the measure of ∠z.

Answers

The measure of ∠x is 60°, and the measure of ∠y is 90°, the measure of ∠z is 30°

What is an angle ?

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

In right angle triangle, Δxyz

Angle ∠x is 60°

Angle ∠y is 90°

It is already known that sum of all the interior angles of any triangle is equal to 180°

So,

∠x + ∠y + ∠z = 180°

60° + 90° + ∠z = 180°

∠z = 30°

Therefore, the third angle is 30°

To know more about angle check:

brainly.com/question/28451077

#SPJ2

This is a right triangle. And every traingle should have total 180°. 180-150 = 30° is the answer

A boy can swim 75 feet in 12 seconds. What is his rate to the nearest mile per hour?

Answers

S=d/t so in this case it's 75/12 which is 6.25. Round it and you got 6 miles per hour.

Answer:

6.25

Step-by-step explanation:

75/12 = 6.25

Y=2x squared +4x-1 . help me

Answers

Answer:

y = 9/8 for part one of solving y in this equation .

Step-by-step explanation:

Answer:

x= (√2y+6/2)-1

Step-by-step explanation:

Swap sides so that all variable terms are on the left hand side.

2x^2+4x−1=y

Subtract y from both sides.

2x^2+4x−1−y=0

Using quadratics formula:

x=-4±√4²-4*2(y-1)/2*2

x= −4±2√2y+6/4

Next solve the equation by using either ± = subtraction or addition

I am using ± = addition. This means I add -4 to 2. From there I simplify equation.

x= (√2y+6/2)-1

Not sure if this means to find x, but I think this is what it would be.

Solve the following equation by transforming it into a perfect square trinomial.* 3x2 + 12x = 63

Answers

$3x^2 + 12x = 63\n \n3x^2+12x-63=0\n \n3(x^2+4x-21)=0\n \n3[x^2+4x+3x-3x-21] =0 \n \n3[x^2+7x-3x-21] =0 \n \n3[x(x +7 )-3(x+7)] =0$

$3 (x +7 ) (x-3) =0 \n \nx+7=0 \ \ \ or \ \ \ x-3 =0\n \nx=-7 \ \ \ or \ \ \ x=3$

Two numbers are randomly selected from integers 1 through 9. What is the probability that only one of the integers is odd given that the sum of the two numbers is odd?1/4

1

40/81

5/40

Answers

Another one where there's a danger of overthinking it !

The sum of ANY two integers is odd only if one is even and one is odd.

If they're both odd OR both even, then their sum is even.

So if their sum is odd, then one is odd and the other is even.

The probability is ' 1 ' (100%) .

Find the median and mean of the data set below:
4, 45, 34, 23, 33