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2 years ago

8

Which steps transform the graph of y=x^2 to y=-(x-3)^2+2

1 answer:

damaskus [11]2 years ago

8 0

Answer:

reflection over the x-axis

shifted 3 right

shifted 2 up

Step-by-step explanation:

This function is quadratic. Quadratic graphs are written as y=a(x-h)^2+k. Where a is a non-zero number that affects the vertical appearance of the graph, h is the horizontal placement, and k is the vertical placement.

When a is negative then, the graph has been reflected over the x-axis. This makes it look like it has been turned upside down. The variable h affects how the x-values are shifted. In this equation, h looks negative but it is actually positive because if you look at the formula, h is being subtracted. Positive h values move the graph right. So, the graph is shifted 3 units to the right. Finally, k does the same thing as h but on the vertical (y) axis. So, +2 makes the graph shift 2 units up.

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3 years ago

The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people.

KonstantinChe [14]

Using an exponential function, the inequality is given as follows:

$9400(0.857)^t < 6000$

The solution is t > 2.9, hence the tax status will change within the next 3 years.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

For this problem, the parameters are given as follows:

A(0) = 9400, r = 0.143.

The population after t years is modeled by:

$A(t) = A(0)(1 - r)^t$

$A(t) = 9400(1 - 0.143)^t$

$A(t) = 9400(0.857)^t$

The tax status will change when:

$A(t) < 6000$

Hence the inequality is:

$9400(0.857)^t < 6000$

Then:

$(0.857)^t < \frac{6000}{9400}$

$\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}$

$t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}$

Since both logs are negative:

$t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}$

t > 2.9.

The solution is t > 2.9, hence the tax status will change within the next 3 years.

More can be learned about exponential functions at brainly.com/question/25537936

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2 years ago

I need help with this now please

Katyanochek1 [597]

I believe it is linear because both numbers on top and bottom go up the exact amount from the beginning to end

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