Tarzan, the story of a man who swings through the trees, has fascinated many of us for many
years. Suppose that Tarzan is in a tree 14 meters above the ground. He must swing on a vine to get to another tree. One second after he begins the swing, he is 10.5 meters above the ground. Three seconds after he begins after he begins the swing, he is 6.5 meters above the ground.
Name the points, write a quadratic equation that would represent the problem and find the lowest point of his swing.
I know the points are: (0, 14) (1, 10.5) (3, 6.5)
and that the equation is y = .5x2 – 4x + 14
but i can't figure out how my teacher got to that equation, can you guys explain? and is the lowest point the vertex because it's a quadratic?
years. Suppose that Tarzan is in a tree 14 meters above the ground. He must swing on a vine to get to another tree. One second after he begins the swing, he is 10.5 meters above the ground. Three seconds after he begins after he begins the swing, he is 6.5 meters above the ground.
Name the points, write a quadratic equation that would represent the problem and find the lowest point of his swing.
I know the points are: (0, 14) (1, 10.5) (3, 6.5)
and that the equation is y = .5x2 – 4x + 14
but i can't figure out how my teacher got to that equation, can you guys explain? and is the lowest point the vertex because it's a quadratic?
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y = .5x2 – 4x + 14
y =0.5{x^2 -8x} +14
= 0.5{x^2 -8 +16} +14 - 0.5(16)
= 0.5(x-4)^2 +14 -8
= 0.5(x-4)^2 +6
Lowest point is (4,6) ..................Ans
The x-axis is time and y-axis height
when x =0 in y =0.5x^2-4x+14, then y =14
when x =1 in y =0.5x^2-4x+14, then y =10.5
when x =3 in y =0.5x^2-4x+14, then y =6.5
y =0.5{x^2 -8x} +14
= 0.5{x^2 -8 +16} +14 - 0.5(16)
= 0.5(x-4)^2 +14 -8
= 0.5(x-4)^2 +6
Lowest point is (4,6) ..................Ans
The x-axis is time and y-axis height
when x =0 in y =0.5x^2-4x+14, then y =14
when x =1 in y =0.5x^2-4x+14, then y =10.5
when x =3 in y =0.5x^2-4x+14, then y =6.5