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andreyandreev [35.5K]
3 years ago
9

PLEASSSSE HELPPP

Mathematics
1 answer:
nikitadnepr [17]3 years ago
4 0
What does Y equal I need that to be able to help you

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find an equation in the form y=ax^2+bx+c for the parabola passing through the points. (2,28),(4,116),(-3,88)
IgorC [24]
<h3>Answer:</h3>

y = 8x² -4x +4

<h3>Explanation:</h3>

I find it quick and easy to let a graphing calculator do quadratic regression on the given points. It gives the coefficients of the equation directly. (See attached.)

_____

If you want to do this "by hand," you can substitute each of the x and y value pairs into the equation to get three linear equations in a, b, and c. These are generally easy to solve, as the "c" variable can be eliminated right away.

<em>For x = 2</em>

... 28 = a·2² +b·2 +c = 4a +2b +c

<em>For x = 4</em>

... 116 = a·4² +4b +c = 16a +4b +c

<em>For x = -3</em>

... 88 = a·(-3)² +b·(-3) +c = 9a -3b +c

Subtracting the first and third equations from the second, we have ...

... (16a +4b +c) -(4a +2b +c) = (116) -(28) ⇒ 12a +2b = 88

... (16a +4b +c) -(9a -3b +c) = (116) -(88) ⇒ 7a +7b = 28

Dividing the first of these reduced equations by 2, and the second by 7, we have ...

  • 6a +b = 44
  • a +b = 4

Subtracting the second of these from the first gives ...

... (6a +b) -(a +b) = (44) -(4) ⇒ 5a = 40

From which we find

... a = 8

... b = 4 -a = 4 -8 = -4

We choose the first of the original equations to find c:

... c = 28 -4a -2b = 28 -4·8 -2(-4)

... = 28 -32 +8 = 4

With (a, b, c) = (8, -4, 4), the equation of the parabola is ...

... y = 8x² -4x +4

5 0
3 years ago
A prism is completely filled with 1120 cubes that have edge lengths of 1/2 in. What is the volume of the prism?
DedPeter [7]

Answer:

Volume of the prism = 140 cubic inches.

Step-by-step explanation:

The edge length of the cube is 1/2 inches.

The volume of the cube is given by

\text{Volume}=(\text{edge})^3\\\\V=(1/2)^3\\\\V=0.125

Now, it has been given that there are 1120 cube is completely filled in the prism. Hence, we have to the multiply the volume by 1120.

Volume of the prism = 1120 × 0.125

Volume of the prism = 140 cubic inches.

6 0
2 years ago
Read 2 more answers
Amy launched a ball into the air. The height of the ball can be represented by the equation h = -16t^2 + 96t + 112, where h is t
Sidana [21]

Answer:

Vertex is (3, 256)

Step-by-step explanation:

The vertex means that at 3 seconds, the highest point the ball will reach is 256 units in the air.

3 0
2 years ago
Write the subtraction expression for the number line shown.
Scorpion4ik [409]

Answer is

0-4-9

start from zero then count

7 0
3 years ago
Read 2 more answers
Given: If a child is at least 4 feet tall, then
KIM [24]

Answer:

F

Step-by-step explanation:

7 0
3 years ago
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