Find the equation of a parabola with a focus at (-4, 7) and a directrix of y=1. ANSWERS ATTACHED, 15 points, due in 2 HOURS!

Solution: y - 4 = 1 / 12(x + 4)² or Option B

Step-by-step explanation:

Since the directrix is vertical, use the equation of a parabola that opens up or down -

(x - h)² = 4p(y - k)

Remember that the vertex, (h, k) is halfway between the directrix and focus. Therefore we can find the  y  coordinate of the vertex using the formula y = y coordinate of focus + directrix / 2.The  x -coordinate will be the same as the  x  coordinate of the focus.

Vertex: (- 4, 7 + 1 / 2) = (- 4,4)

Now we can find the distance from the focus to the vertex. The distance  from the vertex to the directrix is  represented by | p |. We can subtract the  y  coordinate of the vertex from the  y -coordinate of the focus to find  p.

p = 7 - 4 = 3

Substitute the known values for these variables into the given equation (x - h)² = 4p(y - k) to get our solution.

(x + 4)² = 4(3)(y - 4),

(x + 4)² = 12(y - 4)

1 / 12(x + 4)² = y - 4

y - 4 = 1 / 12(x + 4)² ~ As you can see your solution is option b.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

1.30

step-by-step explanation: