Question

The path of a marshmallow launched from a catapult can be modeled by this equation: LaTeX: y=-0.05x^2+x+3\:

y represents the height of the marshmallow, in feet



x represents the horizontal distance from the point it is launched, in feet



How high off the ground (in feet) is the marshmallow as it begins flying? (Hint: this will be the point on the curve where x = 0)







Enter your answer below in decimal form in the simplest way possible. Example answer: 18.2

Answer 1

y = -0.05x^2 +x + 3 relates the height of the marshmallow to the horizontal distance it has travelled. It can be written in function notation as follows:

f(x) = -0.05x^2 + x + 3. To find the initial height of the marshmallow we plug in f(0).

f(0) = -0.05(0) + 0 + 3

f(0) = 3

An alternative way to solve this problem is to just look at the term with no variable attached. This is the initial position.