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inna [77]
3 years ago
13

Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.

Mathematics
1 answer:
Alexus [3.1K]3 years ago
7 0
(x-h)^2=4P(y-k), vertex is (h,k)
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k

nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix

I will only convert the 1st one fully, you should be able to do the rest

1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
 (-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)

k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5

basically completee the square with x and find P by force factoring a 4 out

2.  directix: y=-1.75

3. directix: y=1.5

4. directix: y=17.25

5. d: -37.5

6. d: 9.25

7. d=2.625

order them yourself

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4000
Airida [17]

Answer:

$1000 ; 500 ; 1000 ; y = 500x + 1000

Step-by-step explanation:

From the graph, the initial deposit which started the savings account is $1000 ; this is the value on the y - intercept, the value in the account at time or period = 0.

The slope :

x1 = 0 ; y1 = 1000

x2 = 6 ; y2 = 4000

Slope = Rise / Run

Rise = y2 - y1 = 4000 - 1000 = 3000

Run = x2 - x1 = 6 - 0 = 6

Hence,

Slope = 3000 / 6

Slope = 500

y - intercept = 1000 (from. Graph)

Equation in slope intercept form:

General form : y = mx + c

m = slope ; c = intercept

Equation is written as ;

y = 500x + 1000

5 0
3 years ago
Please help :( Im desperate
ki77a [65]

Answer:

(2,4)

Step-by-step explanation:

When graphed the lines intersect at point (2,4) which is the solution.

8 0
2 years ago
Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle translates 2 units up and 1 unit right. Which rule repres
Nataly [62]

Answer:

The translation statement is given by:

(x,y)\rightarrow (x+1,y+2)

After the translation, the coordinates of vertex A is (-2,6).

Step-by-step explanation:

Given :

Vertices of a triangle ABC are:

A(−3, 4), B(4, −2), C(8, 3)

The triangle is translated 2 units up and 1 unit right.

To find the co-ordinates of point A after translation.

Translation rules.

For shift of c units up, the translation is given as:

(x,y)\rightarrow (x,y+c)

For shift of k units right, the translation is given as:

(x,y)\rightarrow (x+k,y)

So, it says the triangles is translated 2 units up and 1 unit right.

The translation statement is given by:

(x,y)\rightarrow (x+1,y+2)

So, co-ordinates of point A after translation is given by :

(-3,4)\rightarrow (-3+1,4+2)=(-2,6)

After the translation, the coordinates of vertex A is (-2,6).

4 0
3 years ago
What is the recursive rule for the sequence?
adoni [48]
An= -2 (an+1), a1 = 5
5 0
3 years ago
PLEASE HELP WILL GIVE POINTS
Alexxx [7]

The rate of change is meaning the slope. The slope of A is 8, therefore, the answer would be 7.

hope this helps :)

3 0
3 years ago
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