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otez555 [7]
3 years ago
6

PLEASE ANSWER ALL

Mathematics
1 answer:
mars1129 [50]3 years ago
4 0

Step-by-step explanation:

The axis of symmetry: is the line that makes the parabola split in exactly half and lines up with the vertex. For that parabola x=1 is the line of symetry.

The vertex is where the minimum of the graph is, on this graph you can eyeball it to be (1,-9)

The x-intercept is where y is 0 so that's where the lines intersex with the x-axis. (-2,0) and (4,0)

The y-intercept of the function is where x is 0 and where the parabola intersects with the y-axis. On this graph it would be (0,-8)

Hope that helps :)

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1 Without graphing, determine the characteristics of the graph.
olga nikolaevna [1]

Answer: (3, -1)

Step-by-step explanation:

y = |x-3|-1

When y=|x|, vertex is (0, 0).

Now, let's translate the graph so it becomes y = |x-3|-1.

|x| ==> |x-3|         Translate the graph 3 units to the right

Vertex: (0+3, 0) ==> (3, 0)

|x-3| ==> |x-3|-1     Translate the graph 1 unit down

Vertex: (3, 0-1) ==> (3, -1)

Vertex: (3, -1)

7 0
2 years ago
HURRY QUICK!!
antiseptic1488 [7]

After plotting all the three points, we get the parabolic equation in the form is 2(x - 1)²-34.

<h3>What is parabola?</h3>

Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line.

General equation of the quadratic equation,

Y = ax² + bx +c

Given points,

(-2, 0),

(-1, -10),

(4, 0).

Putting the points in the general equation,

Putting (-2, 0), we get

0 = 4a - 2b + c

Putting (-1, -10), we get

-10 = a - b +c

Putting (4, 0), we get

0 = 16a + 4b +c

Solving all equations we get,

a = 2 , b = -4 , c = -16

After putting the values,

Y = 2x²- 4x- 16

2(x² - 2x - 8)

2(x²- 2x + 1 - 1 - 16)

=2(x - 1)²-34

Hence we get the required equation in the parabolic form.

To know more about parabola, visit :

brainly.com/question/21685473

#SPJ1

5 0
1 year ago
For what values of x is f(x) = |x + 1| differentiable? I'm struggling my butt off for this course
pav-90 [236]

By definition of absolute value, you have

f(x) = |x+1| = \begin{cases}x+1&\text{if }x+1\ge0 \\ -(x+1)&\text{if }x+1

or more simply,

f(x) = \begin{cases}x+1&\text{if }x\ge-1\\-x-1&\text{if }x

On their own, each piece is differentiable over their respective domains, except at the point where they split off.

For <em>x</em> > -1, we have

(<em>x</em> + 1)<em>'</em> = 1

while for <em>x</em> < -1,

(-<em>x</em> - 1)<em>'</em> = -1

More concisely,

f'(x) = \begin{cases}1&\text{if }x>-1\\-1&\text{if }x

Note the strict inequalities in the definition of <em>f '(x)</em>.

In order for <em>f(x)</em> to be differentiable at <em>x</em> = -1, the derivative <em>f '(x)</em> must be continuous at <em>x</em> = -1. But this is not the case, because the limits from either side of <em>x</em> = -1 for the derivative do not match:

\displaystyle \lim_{x\to-1^-}f'(x) = \lim_{x\to-1}(-1) = -1

\displaystyle \lim_{x\to-1^+}f'(x) = \lim_{x\to-1}1 = 1

All this to say that <em>f(x)</em> is differentiable everywhere on its domain, <em>except</em> at the point <em>x</em> = -1.

4 0
3 years ago
The large rectangle shown here is 3cm by 5 cm. What is a direct way to determine the area of the rectangle in square centimeters
dlinn [17]

Answer:

Place the squares on the rectangle.

Step-by-step explanation:

Hello!

The area of the 1cm by 1cm square is 1 square cm.

We can solve for the area by placing multiple of those squares in the larger rectangle.

If we place it, we get 15 placed squares, with a total area of 15 square cm. This relies on the meaning of area, as we are simply measuring the number of square cm taken up by the object.

We would place 3 rows of 5 squares, representing a height of 3 cm (side length of 3 squares), and a length of 5 cm (side length go 4 squares).

This also proves the area formula A = L * W, as we multiple the side lengths to find the number of square units.

8 0
2 years ago
A store had 5 packs of paper for $7.80. How much would it cost if you were to buy 3 packs
valentina_108 [34]
To buy 3 packs, the cost would be $4.68
4 0
3 years ago
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