Question

Someone help me please.. Medals?

Answer 1

2.How is the graph y=-8x^2-2 different from the graph of y=-8x^2?
a. It is shifted 2 units to the left
b. it is shifted 2 units to the right
c. it is shifted 2 units up
d. it is shifted 2 units down.


3.A model rocket is launched from a roof into a large field. The patch of the rocket can be modeled by the equation y=-0.8x^2+12x+25.8 where x is horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground.
How far horizontally from its starting point will the rocket land? Round your answers to the nearest hundredth.
a. 25.80 m
b. 37.00 m
c. 17.24 m
d. 16.91 m

Answer 2

Okay, for number 2, think of it this way. When you have an extra -2, and y = whatever minus that extra 2, it means the y ends up being 2 less every time. What's Y? the height, so it would shift 2 units down every time, or D.

Answer 3

Thank you!

Answer 4

Do we not know how high from the ground the roof is? That will affect the answer. Anyway, I think the question is over-simplifying it, so let's do it this way. Number three, it might help to first graph it to understand the problem. Here's the graph.
http://puu.sh/5OJI5.png

So it's asking for how far from the starting point it will land, which will be the distance between where y equals zero, also known as the y intercepts.

How do you find y intercepts? It's whatever plugs in as x to make the y 0.

So our equation is
y=-0.8x^2+12x+25.

0 = -0.8x^2 + 12x + 25
-25 = -0.8x^2 + 12x

Here's where you probably got stuck if you already knew the basics. We need to find a "square" to complete for the equation that would make it work out. Usually we wouldn't have to do this, but since the equation isn't easily completed in the form it was in, we have to.

First, we divided everything by -0.8 to get rid of the nasty decimal and put it in a form we can work with.
31.25 = x^2 -15 x

Now, we divide the -15x by 2, which gives us -7.5
We square -7.5, which gives us 56.25

Add that to both sides
56.25 + 31.25 = x^2-15x+56.25
We know, that since we completed the squares, the equation on the right is also the same as (x-7.5)^2. You can look this up in your lesson if you don't remember.

So 56.25+31.25 = (x-7.5)^2
87.5 = (x-7.5)^2

Now, let's solve for x
First let's take the square root of both sides to simplify.

square root of 87.5 = x-7.5
square root of 87.5 + 7.5 = x

And we know, with a calculator, that the square root of 87.5 + 7.5 is 16.9

This is very close to D, and that's the answer.