# math

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Sam kicks a ball horizontally along a deck that is 5 m
above the ground.
The ball goes off the edge of the deck.
A model for the path of the ball once it leaves the deck is a parabola.
The equation of the parabola is y = ax^2+ bx + c.
The ball hits the ground at a horizontal distance of 3.1 m from the edge of the deck.
Find the values of a, b and c.

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• math -

If y is the height above the ground,
y = 5 when x = 0, so
a*0^2 + b*0 + c = 5,
so c = 5

When x = 0, the slope of the trajectory (path) is zero, so
dy/dx = 2ax + b = 0 at x = 0, so b = 0

When x = 3.1, y = 0, so

a(3.1)^2 +5 = 0
a = -5/(3.1)^2 = -0.521

y = -0.521 x^2 + 5

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