SOLUTION: In 2011, a mobile phone company made a live-action version of the popular Angry Birds game at a park in Barcelona as part of their marketing campaign. During the game, a player lau

Question 1097695: In 2011, a mobile phone company made a live-action version of the popular Angry Birds game at a park in Barcelona as part of their marketing campaign. During the game, a player launched a bird to a maximum height of 12 m above ground. The bird landed 16 m away from its launch platform which is located at ground level. Model the bird�s path using a quadratic function f(x), where x is the horizontal displacement of the bird in meters. Assume that the bird was launched from the origin of the Cartesian plane. Express your answer in standard form.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the vertex form of a quadratic equation is y = a * (x-h)^2 + k

(h,k) is the vertex of the equation.

you are given that the maximum height is 12 and that the zero crossing points are x = 0 and x = 12.

this makes the vertex of the quadratic equation equal to (6,12).

in the equation of y = a * (x-h)^2 + k, replace h with 6 and k with 12 to get:

y = a * (x-6)^2 + 12

the value of y is 0 when x is equal to 0 or x is equal to 12.

when x = 0, you get:

0 = a * (0-6)^2 + 12 which becomes 0 = a * (-6)^2 + 12 which becomes 0 = 36a + 12.

solve for a to get a = -1/3.

when x = 12, you get:

0 = a * (12-6)^2 + 12 which becomes 0 = a * (6)^2 + 12 which becomes 0 = 36a + 12.

solve fora to get a = -1/3.

the vertex form of the equation becomes y = -1/3 * (x-6)^2 + 12.

the graph of that equation is shown below:

$$$

you can convert this vertex form of the equation into the standard form of the equation by simplifying it.

start with y = -1/3 * (x-6)^2 + 12
simplify to get y = -1/3 * (x^2 - 12x + 36) + 12
simplify further to get y = -1/3 * x^2 + 4x - 12 + 12
simplify further to get y = -1/3 * x^2 + 4x

that's the standard form of the equation.

the graph of that equation is shown below:

$$$

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