What is the vertex of the parabola whose equation is y = (x + 1)2 + 3? (-1, -3) (-1, 3) (1, 3)

Answers

Answer 1

Answer: Algebra:
A standard parabola is y = x^2. Its vertex is at (0,0)
You can change the position (or vertex) of the parabola.
To move a parabola across the x-axis, you can add or subtract a number from x WITHIN brackets of the ^2
eg. (x + 1)^2 will move the parabola across the x-axis. It will move is one unit to the LEFT (as the sign is opposite to the direction it moves ie. The sign it + but you move the whole parabola in the -ve direction).
Adding or subtracting a number from x OUTSIDE of the ^2 moves the parabola up or down the y-axis
eg. x^2 + 3 will move the parabola UP 3 units (the sign is the same as the direction it moves when the added/subtracted number is outside of the ^2 ie. the sign is positive so the parabola moves up in the positive direction)

From this, we can conclude that because (x + 1)^2 + 3, the vertex will be where x = -1 and where y = 3

Vertex : (-1,3)

Calculus:
f(x) = (x + 1)^2 + 3 = x^2 + 2x + 1 + 3 = x^2 + 2x + 4
Expanding the formular to make it easier to differentiate

f'(x) = 2x + 2
Differentiating (finding the formular the the gradiet of the parabola)

0 = 2x + 2
When the gradient is equal to zero, it must be the vertex

-2 = 2x
-2/2 = x
x = -1
Solve to give the x value at the vertex

f(x) = (x + 1)^2 + 3
= (-1 + 1)^2 + 3
Substitute x = -1 into original equatiom to find y value at the vertex

= (0)^2 + 3
= 0 + 3
= 3
Solve for y

Vertex : (-1,3)

Answer 2

Answer:

Answer:

Vertex : (-1,3) is the answer

Hope this helped!!!!

Step-by-step explanation:

Related Questions

What is 3 1/4 minus 2 1/2?
Which sentence fully illustrates that polygon ABCD is congruent to polygon PQRS?
Martin has 5/6 of a pizza Liam has four times as much pizza is Martin how much pizza does Liam have? (Put it in a fraction)
There is 1 other part to this pls help asap
Lltyflyhighll1Identify a transformation of the function f(x)=|x| by observing the equation of the function g(x)=|x|-32A vertical shift 32 units upward.A horizontal shift 32 units to the right.A vertical shift 32 units downward.A horizontal shift 32 units to the left

Use parentheses to make the equation true: 9-8x2-1=3

Answers

try all ways to finish the answer example:
(9-8)*2-1=1
9-(8*2)-1=-8
9-8*(2-1)=1
all answers dont equal up to 3
and because there is no possible solution this is a troll question

There are 5 cakes in a box.The box and cakes weigh 300 grams altogether.
The box weighs 25 grams.
Each cake weighs the same.
What does each cake weigh? |
grams.

Help!!!

Answers

Answer:

35g

Step-by-step explanation:

given,altogether 300g

box weight is 25 gram

know we know that

1 cake weight and box =300/5

1 cake weight =60 gram -25gram

cake weight =35g

The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:High Low Q1 Q3 IQR Median Mean σ
College 20 6 8 18 10 14 13.3 5.2
High School 20 3 5.5 16 10.5 11 11 5.4

Which of the choices below best describes how to measure the spread of this data?
A. Both spreads are best described with the IQR.
B. Both spreads are best described with the standard deviation.
C. The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
D. The college spread is best described by the standard deviation. The high school spread is best described by the IQR.

Answers

Answer:

C. The college spread is best described by the IQR. The high school spread is best described by the standard deviation.

Step-by-step explanation:

If data is normally distributed we use Standard deviation otherwise we use Interquartile Range (IQR) for measuring the spread.

Further, data is said to be normally distributed if Mean = Median = Mode.

So, High School data is normally distributed but College data is not.

So, We measure the spread of College data by IQR and High School data by Standard Deviation.

Thus, Option C is the only correct option.

A 12-gallon tub has a faucet that lets water in at a rate of 3 gallons per minute, and a drain that lets water out at a rate of 1.5 gallons per minute. If you start with 3 gallons of water in the tub, how long will it take to ﬁll the tub completely?

Answers

Vol of water required to fill up the tub = 12-3 = 9
Rate of water per min =    3 -1.5 = 1.5/min
Using the formula           vol   =   rt
                                            t = v/r
                                            t =    9/1.5    =   6
time taken =    6 mins

Why is it a good idea to check to see if your answer is reasonable?a. if your answer is reasonable, you have probably done the problem correctly
c. you just need to solve for the variable
b. if you understand the problem, you will not need to check your answer
d. to get the correct answer, you will need to draw a picture
Mark this and return

Answers

Answer:

Option: a is the correct answer.

a. if your answer is reasonable, you have probably done the problem correctly.

Step-by-step explanation:

Checking for reasonableness is a process by which students evaluate estimations to see if they are reasonable guesses for a problem.

So, a good idea to check to see if your answer is reasonable is:

a. if your answer is reasonable, you have probably done the problem correctly.

( Since a reasonable answer is just a estimation of the problem it can't be claimed to be true but it is just a probable estimation ).

It is a good idea to check to see if your answer is reasonable because a. if your answer is reasonable, you have probably done the problem correctly.

The sum of two numbers is 58.the smaller number is 12 less than the larger number.what are the numbers?