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3 years ago

6

Natalia bought 8 glitter wands for 50$

1 answer:

kirza4 [7]3 years ago

4 0

Answer:

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What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

telo118 [61]

Answer:

$f(x)=-\frac{1}{8}(x-3)^2+3$

Step-by-step explanation:

We want to find the equation of the parabola with a focus of $(3,1)$ and directrix $y=5$ .

Considering the directrix, the quadratic graph must open downwards.

The equation of this parabola is given by the formula,

$(x-h)^2=4p(y-k)$ , where $(h,k)$ is the vertex of the parabola.

The axis of this parabola meets the directrix at $(3,5)$ .

Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,

$h=\frac{3+3}{2}=3$ and $k=\frac{5+1}{2}=3$ .

The equation of the parabola now becomes,

$(x-3)^2=4p(y-3)$ .

Also $|p|$ is the distance between the vertex and the directrix.

$|p|=2$

This implies that $p=-2\:or\:2$ .

Since the parabola turns downwards,

$p=-2$ .

Our equation now becomes,

$(x-3)^2=4(-2)(y-3)$ .

$(x-3)^2=-8(y-3)$ .

We make y the subject to get,

$y=-\frac{1}{8}(x-3)^2+3)$ .

This is the same as

$f(x)=-\frac{1}{8}(x-3)^2+3)$ .

4 0

3 years ago

Please answer these three questions. There are 3 images attached below and they apply to each question, in order.

statuscvo [17]

1a. It is because each x only has 1 y and it has an equation
1b. It is not a function because each x has more than 1 y.
1c. It is not a function because there can be no equation written for this graph.

7 0

4 years ago

What is the average rate of change of the function from x = 0 to x = 2?.

irina1246 [14]

The average rate of change of the function from x = 0 to x = 2 is -2

From the complete question (see attachment), we have the following ordered pair when x = 0 and x = 2

$(x,y) = \{(0,10)\ (2,6)\}$

The average rate of change is calculated using:

$\Delta x = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$\Delta x = \frac{6-10}{2-0}$

Evaluate common terms

$\Delta x = \frac{-4}{2}$

Divide -4 by 2

$\Delta x = -2$

Hence, the average rate of change of the function from x = 0 to x = 2 is -2

Read more about rate of change at:

brainly.com/question/8728504

5 0

2 years ago

Find the median of the data in the box plot below.

Bumek [7]

Answer:

Median = 6.5 or 6 1/2

HOPE THIS HELPED! HAVE A GREAT DAY! :)

5 0

3 years ago

Dylan read his book for 2 2/3 hours and Faith read her's for 1 1/5.How much longer did did Dylan read then Faith?

Damm [24]

Answer:

1 7/15

Step-by-step explanation:

2-1=1

then you make 2/3 and 1/5 have the same denominator -

5*3=15

?/15 ?/15

multiply 2 by 5 which is 10, so 10/15

then multiply 1 by 3 which is 3/15

subtract 3/15 from 10/15 which is 7/15

4 0

3 years ago