If A ⊂ B, then which of the following describes the relationship between A and B?

Write a quadratic function in vertex form whose graph has the vertex (-3,5) and passes through the point (0,-14)

dsp73

Answer:

f(x) = -19/9(x + 3)² + 5

Step-by-step explanation:

Given the vertex, (-3, 5) and the point, (0, 14):

Use the following quadratic equation formula in vertex form:

f(x) = a(x - h)² + k

where:

(h, k) = vertex

a = determines whether the graph opens up or down, and makes the graph wide or narrow.

h = determines how far left or right the parent function is translated.

k = determines how far up or down the parent function is translated.

Plug in the values of the vertex, (-3, 5) and the given point, (0, 14) to solve for a:

f(x) = a(x - h)² + k

14 = a(0 + 3)² + 5

14 = a(3)² + 5

14 = a(9) + 5

Subtract 5 from both sides:

-14 - 5 = 9a

-19 = 9a

Divide both sides by 9 to solve for a:

-19/9 = 9a/9

-19/9 = a

Therefore, the quadratic function in vertex form is:

f(x) = -19/9(x + 3)² + 5

Please mark my answers as the Brainliest, if you find this helpful :)

5 0

3 years ago

Kelly's parents plan to put money into an account and leave it there for 16 years before she goes to college. If they put $1000

earnstyle [38]

In 16 years if her parents put in $1,000 and accrues 3.75% interest annually; in 16 years she will have $1,600 in the account.

To find this we need to multiply the amount deposited originally, by the annual percentage, by the amount of years in total.

We'll change the percentage into a decimal by moving the decimal two places to the right; which will change it to 0.0375.

Our equation will look like this:

1,000 x 0.0375 x 16

1,000 x 0.0375 = 37.50

37.50 x 16 = 600.

So, in 16 years at 3.75%, she will earn $600 in interest.

We'll add the interested of $600 to the original deposited amount of $1,000.

$1,000 + $600 = $1,600.

7 0

3 years ago

Please answer this correctly

dimulka [17.4K]

Answer:

ok honestly that wus super confusing, but i think its a trick question so the answer is 0

Step-by-step explanation:

3 0

3 years ago

PLS HELP NEEDED ASAP GIVING BRAINLESS

Svetllana [295]

The answer would be b

8 0

3 years ago

Which of the following does not represent an attribute of the function f(x) = [x]?

luda_lava [24]

Answer: The graph has a line of symmetry at y = 0.

Step-by-step explanation:

I suppose that this refers to the function:

f(x) = IxI

The parent absolute value function.

Remember how this works:

IxI = x if x ≥ 0

IxI = -x if x ≤ 0.

Let's analyze the sentences:

1) "The x- and y-intercepts are (0,0)"

This is true, when x = 0 we have:

y = f(0) = I0I = 0

So the point (0, 0) is the only x-intercept and the only y-intercept.

2) "Domain: (-∞,∞); Range: [0,∞)"

This is also true, we clearly do not have any restriction in the domain.

And when looking at the range, we can see that the possible values of y are always positive or zero.

3) "(0, 0) is the minimum point."

Now, as x increases in the positive range, also does the value of y.

And as x decreases in the negative range, as the absolute value changes the sign, we will also have an increase in the value of y.

Then we have that (0, 0) must be the minimum.

4) "The graph has a line of symmetry at y = 0."

This is false.

The real line of symmetry is at x = 0, y = 0 corresponds to the x-axis, and as the graph opens up, we can not have symmetry about any line parallel to the x-axis.

4 0

4 years ago

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