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adoni [48]
3 years ago
9

Estelle is raking leaves in her yard. After 1 hour, she has 2 bags of leaves. After 3 hours, she has 6 bags of leaves. Which gra

ph represents Estelle's leaf raking progress?
Answers:
graph of line going through (0, 0) with a slope of 2
graph of line going through (0, 2) with a slope of 2
graph of line going through (0, 0) with a slope of 3
graph of line going through (0, 3) with a slope of 3
Mathematics
1 answer:
denis-greek [22]3 years ago
7 0
The graph with the line going through (0,0) with a slope of 2. This is because for every 1 hour, she has 2 bags of leaves.
The y number goes up by 2. 0 hours, 0 bags. 1 hour, 2 bags. 2 hours, 4 bags. And so on.
(0,0), (1,2), (2,4), (3,6)...
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Answer:

y = (x - 3)^2 - 12

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Step-by-step explanation:

Given

y = x^2 - 6x - 3

Solving (a): In vertex form

The vertex form of an equation is:

y = a(x - h)^2 + k

To do this, we make use of completing the square method.

We have:

y = x^2 - 6x - 3

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Take the coefficient of x (i.e. -6)

Divide by 2; -6/2 = -3

Square it: (-3)^2 = 9

Add and subtract the result to the equation

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y = x^2 - 6x - 3

y = x^2 - 6x + 9 - 9 - 3

y = x^2 - 6x + 9 - 12

Factorize x^2 - 6x + 9

y = x^2 - 3x-3x + 9 - 12

y = x(x - 3)-3(x - 3) - 12

Factor out x - 3

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y = (x - 3)^2 - 12

Hence, the vertex form of y = x^2 - 6x - 3 is: y = (x - 3)^2 - 12

Solving (b): State the coordinates of the vertex.

In y = a(x - h)^2 + k; the vertex is: (h,k)

The vertex of y = (x - 3)^2 - 12 will be (3,-12)

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