A. True

Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.

Nezavi [6.7K]

Answer: 1) Vertex: (6, -2) Focus: (6, -7/4) Directrix: y = -9/4

2) Vertex: (-2, -1) Focus: (-7/4, -1) Directrix: x = -9/4

<u>Step-by-step explanation:</u>

Rewrite the equation in vertex format y = a(x - h)² + k or x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

(h, k) is the vertex
p is the distance from the vertex to the focus
-p is the distance from the vertex to the directrix

$\bullet\quad a=\dfrac{1}{4p}$

1) y = x² - 12x + 34

$y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}$

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2) x = y² + 2y - 1

$x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}$

4 0

3 years ago

Mr.Bruns class is taking a field trip to the planetarium. The trip will cost $27 for each student. There are 18 students in his

padilas [110]

Total cost
=$27x 18
=$486

4 0

4 years ago

Read 2 more answers

5+ =83 can someone help me out

enot [183]

You can do
83 - 5 to find the answer
So that's
78 or
5 + 78 = 83

4 0

3 years ago

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2. Suppose over several years of offering AP Statistics, a high school finds that final exam scores are normally distributed wit

nirvana33 [79]

Answer:

By the Central Limit Theorem, the mean is 78, the standard deviation is $s = \frac{6}{\sqrt{n}}$ and the shape is approximately normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 78 and a standard deviation of 6

This means that $\mu = 78, \sigma = 6$

Samples of n:

This means that the standard deviation is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{n}}$

What are the mean, standard deviation, and shape of the distribution of x-bar for n?

By the Central Limit Theorem, the mean is 78, the standard deviation is $s = \frac{6}{\sqrt{n}}$ and the shape is approximately normal.

6 0

3 years ago

Which of the following points lies on the graph of the function y = 8x?

nignag [31]

Y = 8^x
For (0, 1): 1 ≠ 8^0 = 1
For (8, 1): 1 ≠ 8^8 = 16,777,216
For (2, 64): 64 = 8^2
For (0, 8): 8 ≠ 8^0 = 1

Therefore, option 3, (2, 64) is the correct answer.

8 0

3 years ago

Read 2 more answers