SOS I'm terrible at math.

1 answer:

5 0

<span>y = -5 cos x is a basic (simple) variation of the basic trig function y = cos x.

The given </span>y = -5 cos x could be re-written as <span>y = -5 cos 1x.
Compare this to the most general form: y = a cos bx.

Here we see that the coefficient b equals 1.

There is a rule for finding the period of such a function: Period = 2pi/b.

Since b = 1 here, the Period here is 2pi/1, or simply 2pi.

Please stop saying "I'm terrible with math." That does not help you at all. Say, instead, "With just a little help I could understand this just fine."</span>

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3 years ago

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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.

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

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,

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

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This equation is now in the form,

$y = a {x}^{2} + bx + c$
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3 years ago

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