4 years ago

Is it linear, quadratic or exponential Please help me thank you

Mathematics

1 answer:

12345 [234]4 years ago

5 0

Answer:

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Step-by-step explanation:

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A. a scientist is studying the change in population for two species of fish in a lake. The table shows how the numbers of each s

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The data can be modeled using linear equatins, because there's the same amount of population for fish A (+20 per year) and fish B (+30 per year) every year.

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3 years ago

Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ

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PART A

The equation of the parabola in vertex form is given by the formula,

$y - k = a {(x - h)}^{2}$

where

$(h,k)=(1,-2)$

is the vertex of the parabola.

We substitute these values to obtain,

$y + 2 = a {(x - 1)}^{2}$

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.

$6 + 2 = a {(3 - 1)}^{2}$

$8= a {(2)}^{2}$

$8=4a$

$a = 2$
Hence the equation of the parabola in vertex form is

$y + 2 = 2 {(x - 1)}^{2}$

PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

$y + 2 = 2{(x - 1)}^{2}$

This implies that

$y + 2 = 2(x - 1)(x - 1)$

We expand to obtain,

$y + 2 = 2( {x}^{2} - 2x + 1)$

This will give us,

$y + 2 = 2 {x}^{2} - 4x + 2$

$y = {x}^{2} - 4x$

This equation is now in the form,

$y = a {x}^{2} + bx + c$
where

$a=1,b=-4,c=0$

This is the standard form

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3 years ago

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Andreyy89

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