MATHEMATICS MIDDLE SCHOOL

Identify the​ vertex, the axis of​ symmetry, the maximum or minimum​ value, and the range of the parabola.yequalsxsquaredplus2xplus1
The vertex is
nothing. ​(Type an ordered​ pair.)

Answers

Answer 1
Answer:

Answer:

Vertex = (-1, 0)

The axis of symmetry is x = -1

Minimum point is (-1, 0)

Range is y ≥ 0

In the interval notation [0, ∞)

Step-by-step explanation:

The given function is y = x^2 +2x + 1.

Write the given equation in the form of y = (x -h)^2 + k.

Here (h,k) is the vertex.

y = x^2 + 2x + 1

y = (x + 1)^2

Vertex = (-1, 0)

Axis of symmetry

The axis of symmetry splits the parabola in 2 equal parts.

In this equation, the axis of symmetry is x = -1

Maximum/minimum value

The parabola goes maximum when there is negative sign, it goes minimum when there is positive sign.

Here we have positive sign in front of (x + 1)^2, therefore, it is minimum at

y= 0

When y =0, x = -1

Therefore, minimum point is (-1, 0)

Range

Y- axis represents the range.

Here the minimum is 0, the maximum goes upto infinity.

Range is y ≥ 0

In the interval notation [0, ∞)

Herewith I have attached the graph of the function.
Answer 2
Answer: Y = x^2 + 2x + 1
Convert to vertex form by completing the square
(2/2)^2 = 1
(X^2+2x+1) -1 +1
Y = (X + 1)^2
The vertex is (1,0) because we have no + q, and we have 1 as our p, and since I don’t know any of the points in order to figure out the vertical stretch, this is the final answer.

Hope this helped!!!

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a store advertises that customers can take 25%off the original price and then take an extra 10%off is this 35% of? explain

Answers

No, it is not 35% off... Let me explain.  Let's say the original price is $100 to make the math easy.  When you take 25% off then take an additional 10% off, the 10% is off of the discounted price, so

100 x 25% = 100 x .25 = 25 dollar discount
New price = $75

Now 10% off of $75
10% x 75 = .10 x 75 = $7.50 discount
New price = 75 - 7.50 = $67.50


Now, if you just took 35% off of $100

100 x 35% = 100 x .35 = $35 discount
New Price = 100 - 35 = $65

Bottom line... when you take an "extra" percentage off, you are taking a percentage of a smaller number, so the discount is not as big.

Write the equation in function form.then graph the equation

x-3y=-9 ???

Answers

x-3y=-9 \n \n-3y=-x -9 \ \ / :(-3) \n \ny=(1)/(3)x + 3

How can you use models to find factor

Answers

Yes, it depends on what kind of model

Craig drank two 5-cup bottles of water in one day how many fluid onces is that

Answers

There are 8 fl oz in 1 cup. First we need to figure out how many cups he drank (multiply 5 by 2). Then multiply how many cups he drank (10) by how many fl oz are in a cup (8). There are 80 fluid ounces in 10 cups of water :)
The answer would be 80 because there are 8 oz. in a cup, so you would do 8x5 for the first bottle which is 40. You would then double 40 to get both of the water bottles. 40x2= 80.

0.7777…=7/9
Use this fact to show that 0.077777...=7/90

Answers

Step-by-step explanation:

Here we have , 0.7777…=7/9 . And using this fact we need to find show that

0.077777...=7/90 . Let's show this:

In the equation 0.077777...=7/90 , Let's evaluate RHS :

⇒ 0.077777

⇒ (0.77777)/(10)

But According to question , 0.7777…=7/9  , So

⇒  (0.77777)/(10)

⇒  ((7)/(9))/(10)

⇒  (7)/(9) ((1)/(10) )

⇒  (7)/(90)

Since , RHS=LHS . Therefore,  0.077777...=7/90 is proved using fact 0.7777…=7/9 .

Y = −x + 2y = 3x + 1

Which description best describes the solution to the system of equations?


line y=-x+2 intersects line y=3x+1.
Lines y=-x+2 and y = 3x + 1 intersect the x axis
lines y=-x+2 and y 3x+ 1 intersect the y-axis

Line y=-x+2 intersects the origin

Answers

line y=-x+2 intersects line y=3x+1.

this is right ↑ I took the test myself and was a little unsure bc some people were saying it was 'lines y=-x+2 and y=3x+1 intersect the y-axis' but it is actually A! Thanks so much! Have a great day!
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