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Vertex word problems
1. Find an equation for the parabola with vertex (-6, -2) that passes through the point ( -3, -11)
Y = a(x-h)^2 + k
-11 = a(-3+ 6)^2 -2
Vertex (-6, -2) (h, k)
Point ( -3, -11) (x, y)
-11 = a(3)^2 - 2
-11 = a(9) - 2
-11 + 2 = a(9) - 2 + 2
-9 = 9a
-9 = 9a
9 9
-1 = a
Y = -(x + 6)^2 -2
Equation for the parabola
2. The path of a football is modelled by the relation where d is the horizonatl distance, in metres, and h is the height of the baseball, in metres, above ground
a) Sketch the path of the footbool
b) What is the maximum height of the football?
c) What is the horizontal distance when this occurs?
d) What is the height of the football at a horizontal distance of 10cm?
Y - axis
X - axis
The maximum height is the optimal value, so it's apart of the vertex. The vertex is the maximum or minimum point on the graph.
The vertex is (12, 26) and the maximum height is the optimal value which is 36.
Maximum height = 36m
The horizonatal distance is the A.O.S, so it's the highest x-axis which is 12.
Horizonatal distance = 12m
Here they tell you the distance, so you substitute the d as 10 and solve
Therefore, the height of the football a horizontal distance of 10cm is 36.
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