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Simora [160]
3 years ago
7

What is the equation, in standard form, of a parabola that models the values in the table?

Mathematics
1 answer:
love history [14]3 years ago
3 0

Answer:

<u>Y=4x^2+3x-6</u>

Step-by-step explanation:

For the standard form equation to model the values in the table, each value of x in the table should give the matching the y value when substituted into the equation. We will test each equation:

<u>Y=3x^2+4x-6 for (-2,4)</u>

Y=3(-2)^2+4(-2)-6=3(4)+-8-6=12+-8-6=-2\\

This does not give 4 as the answer and is not a solution.

<u>Y=4x^2+3x-6 for (-2,4)</u>

Y=4(-2)^2+3(-2)-6=4(4)+-6-6=16+-6-6=-4\\

This does give 4 as the answer and is a possible solution.

<u>Y=4x^2-3x-6 for (-2,4)</u>

Y=4(-2)^2-3(-2)-6=4(4)+6-6=16+6-6=16\\

This does not give 4 as the answer and is not a solution.

<u>Y=-4x^2-3x-6 for (-2,4)</u>

Y=-4(-2)^2-3(-2)-6=-4(4)+6-6=-16+6-6=-16\\

This does not give 4 as the answer and is not a solution.

The only possible solution is <u>Y=4x^2+3x-6</u>

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Answer:

D

Step-by-step explanation:

Exponential equation takes the form  y=a*b^x  where

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  2. b is the base ( b ≠ 1)

The equation given in the problem can be written as  y=-4.8*4^x, so it is <em>an exponential equation, </em>  where a = -4.8 and b = 4.

Thus we can say that the initial value = -4.8 and the base is 4

The correct answer is  D

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11111nata11111 [884]

we have

A(-2, 2),B(6, 2),C(0, 8)

see the attached figure to better understand the problem

we know that

The perimeter of the triangle is equal to

P=AB+BC+AC

and

the area of the triangle is equal to

A=\frac{1}{2}*base *heigth

in this problem

base=AB\\heigth=DC

we know that

The distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Step 1

<u>Find the distance AB</u>

A(-2, 2),B(6, 2)

Substitute the values in the formula

d=\sqrt{(2-2)^{2}+(6+2)^{2}}

d=\sqrt{(0)^{2}+(8)^{2}}

dAB=8\ units

Step 2

<u>Find the distance BC</u>

B(6, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0-6)^{2}}

d=\sqrt{(6)^{2}+(-6)^{2}}

dBC=6\sqrt{2}\ units

Step 3

<u>Find the distance AC</u>

A(-2, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0+2)^{2}}

d=\sqrt{(6)^{2}+(2)^{2}}

dAC=2\sqrt{10}\ units

Step 4

<u>Find the distance DC</u>

D(0, 2),C(0, 8)

Substitute the values in the formula

d=\sqrt{(8-2)^{2}+(0-0)^{2}}

d=\sqrt{(6)^{2}+(0)^{2}}

dDC=6\ units

Step 5

<u>Find the perimeter of the triangle</u>

P=AB+BC+AC

substitute the values

P=8\ units+6\sqrt{2}\ units+2\sqrt{10}\ units

P=22.81\ units

therefore

The perimeter of the triangle is equal to 22.81\ units

Step 6

<u>Find the area of the triangle</u>

A=\frac{1}{2}*base *heigth

in this problem

base=AB=8\ units\\heigth=DC=6\ units

substitute the values

A=\frac{1}{2}*8*6

A=24\ units^{2}

therefore

the area of the triangle is 24\ units^{2}

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