A frog leaps from a stump 4 feet high and lands 6 feet from teh base of the stump. we can consider the initial position of the frog to be (0,4) and its landing to be (6,0).
the height of the frog in feet is given by the following equation: -1/3x^2+4/3x+4
1. what is the horizontal distance (x) from the base of the stump when the frog reached maximum height?
2. what was the maximum height

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- anonymous

The maximum height is found at the vertex of the parabola. You have a parabola when you have an x^2 term as the highest degree.
The vertex is found at -b/2a this happen to be the horizontal distance. what would -b/2a be?

- anonymous

Are you in Algebra or Calculus? This is an algebraic way of doing it.

- anonymous

algebra

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- anonymous

OK.. so let's do it this way.
a = -1/3
b = 4/3
-b/2a = -4/3 over -2/3 ok so far?

- anonymous

ok got ya

- anonymous

When you divide by a fraction, you multiply by the reciprocal.
-4/3 * -3/2 = 12/6 = 2
so x = 2 that is how far away from the stump you are when the the frog is at it's maximum

- anonymous

so the vetex is 2 and thats the horizontal distance?

- anonymous

f
f f
f f
s f
f
--------- f-------------ground
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x = 2

- anonymous

Does my picture make sense... kind of dumb I know

- anonymous

no that really helps

- anonymous

The x value of the vertex is 2 and that is the horizontal distance, now we need to find how high it is at x = 2
Substitute 2 into your equation and find y

- anonymous

y=5.3?

- anonymous

or is it y=8

- anonymous

y = 5.3 I think...
(-1/3)*4 + (4/3)*2 +4
-4/3 + 8/3 + 4
4/3 + 4
5 1/3
Notice the vertex (which is the highest point) has coordinates (2,5.3)

- anonymous

ok think i got ya

- anonymous

ok think i got ya

- anonymous

how would u sketch a graph of this problem

- anonymous

Use your xy coordinate graph paper.
put a dot on (0,4) that is the frog.
Put a dot on (6,0) that is where the frog lands
Put a dot on (2,5.3) that is the highest point.
Draw an arc "like throwing a ball up in the air" to the highest point and then down to the (6,0) point. Like a ball would look like if you were throwing it.

- anonymous

ok thank u i thought it would be an arc

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