All categories

3 years ago

How do you write the equation of this description: the graph of a parabola has a vertex of (2,3) and vertically stretched by 3

Mathematics

1 answer:

Mademuasel [1]3 years ago

3 0

The equation of parabola is y = 3x²- 12x+ 15.

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

The equation of the parabola is given as y = x².

If it has a vertex then the equation can be written as,

y = a(x-h)² + k

where (h, k ) is the vertex and a is the stretching or compressing factor.

So here the vertex is (2,3) and it is vertically stretched by 3.

So the equation is given as,

y = 3(x-2)² + 3

y = 3(x² -4x+4) + 3

= 3x² - 12x + 12 + 3

y = 3x²- 12x+ 15 is the equation of the parabola.

You might be interested in

Plot (25/3) and (42/3) on the number line.

ss7ja [257]

Answer:

Refer to the Attachment

Step-by-step explanation:

Rewriting the fractions in decimal and whole number, we have the following:

$\frac{25}{3} = 8\frac{1}{3} = 8.3$

$\frac{42}{3} = 14$

Thus, 42/3 is on 14 and 25/3 is on 8 and then add 1/3 from 8 going to 9.

Therefore, the points must be plotted as follows:

The blue point indicates the 42/3 while the red point indicates the 25/3.

8 0

3 years ago

What is the slope of the line that passes through the points

Whitepunk [10]

Answer:

-5/2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-29-(-9))/(15-7)

m=(-29+9)/8

m=-20/8

simplify

m=-5/2

8 0

4 years ago

Read 2 more answers

Question 24 (1 point)

Aleksandr-060686 [28]

9514 1404 393

Answer:

(a) y = 5

Step-by-step explanation:

The equation of a horizontal line can be written as ...

y = constant

In order to make that line pass through a given point, the constant must match the y-coordinate of the point. Here, that is 5.

y = 5

7 0

3 years ago

Each problem below gives the endpoints of a segment. Find the coordinates of the midpoints of each segment. A.(5, 2) and (11, 14

kvv77 [185]

The midpoints are (8,3) and (6.5,6).

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

Midpoint formula = ((x1+x2)/2 , (y1+y2)/2)

(x1,y1) = (5,2)

(x2,y2) = (11,4)

Midpoint = ((5+11)/2 , (2+4)/2)

⇒ ((16/2) , (6/2))

⇒ (8,3)

(x1,y1) = (3,8)

(x2,y2) = (10,4)

Midpoint = ((3+10)/2 , (8+4)/2)

⇒ ((13/2) , (12/2))

⇒ (6.5,6)

8 0

4 years ago

In 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent (Pew Research, June 5, 2014). An independe

enot [183]

Answer:

$n = (\frac{z\sqrt{0.16*0.84}}{0.03})^2$ , in which z is related to the confidence level.

b) A sample size of 991 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent

This means that $\pi = 0.16$

a. What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03 (round up to the next whole number).

This is n for which $M = 0.03$ . So