A: To find the frog's max height, we need to find the vertex of the parabolic equation h = -0.5d^2 + d + 4. The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula x = -b / (2a). In this case, a = -0.5 and b = 1.
Therefore, the x-coordinate of the vertex is:
d = -1 / (2*(-0.5)) = 1
Now, we can find the max height by plugging d = 1 into the equation:
h = -0.5(1)^2 + 1 + 4 = -0.5 + 1 + 4 = 4.5 feet
So, the frog's max height was 4.5 feet.
B: To find how far from the stump the frog landed, we need to find the horizontal distance when the frog's height is 0. This can be solved by setting h = 0 and solving for d:
0 = -0.5d^2 + d + 4
d^2 - 2d - 8 = 0
(d - 4)(d + 2) = 0
This equation gives us two possible values for d: d = 4 or d = -2. Since distance can't be negative, the frog landed 4 feet from the stump.
C: The horizontal distance from the stump at the frog's max height can be found by plugging d = 1 into the equation:
h = -0.5(1)^2 + 1 + 4 = 4 feet
Therefore, the frog's horizontal distance from the stump at her max height was 1 foot.
A frog sitting on a stump 4 feet high hops off and lands on the ground. During her leap, the frog's height h in feet is given by the equation h= - 0.5d^2+d+4, where d is the horizontal distance in feet from the base of the stump.
A: What was the frog's max height?
B: How far from the stump did the frog land?
C: What was the frog's horizontal distance from the log at her max height?
1 answer
1 answer