The vertex of this parabola is at (-3, 6). which of the following could be its equation?
A. y=-3(x-3)^2+6
B. y=-3(x+3)^2+6
C. y=-3(x-3)^2-6
D. y=-3(x+3)^2-6

Option B -  y=-3(x+3)^2+6

Step-by-step explanation:

Step 1:

The equation of any parabola in the standard form with vertex at the origin is y^2 = 4ax  . When it opens upward, the equation would be x^2 = 4ay

When the vertex is shifted to a point other than the origin, the equation would be

(x-h)^2 = 4a(y-k)

Step 2 :

Given that the vertex of the parabola is at  (-3, 6). We will have the x and y co-ordinate shifted with this value.

So the equation of the parabola will have x and y shifted to x-(-3)) and y-6

=> x+3 and y-6

Step 3:

Based on the above 2, we can see that option B  y=-3(x+3)^2+6 could be the equation of the parabola.

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.

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