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scZoUnD [109]
3 years ago
8

A ball is thrown from the top of a hill. The graph shows the relationship between the height h, in meters, of the ball above the

ground at the base of the hill and the time t, in seconds, after the ball is thrown. The function h(t) = -4.9t2 + 9.8t + 15 models h as a function of t. What is the significance of the vertex of the parabola in terms of height and/or time?
Mathematics
2 answers:
Nataliya [291]3 years ago
5 0

Answer:

The maximum height of the ball is 19.9 meters after 1 second.

Step-by-step explanation:

The height of a ball represents by the function

h(t) = -4.9t2 + 9.8t + 15

where, h(t) is the height in meters, of the ball above the ground at the base of the hill and the time t, in seconds, after the ball is thrown.

In the given equation leading coefficient is -4.9 which is a negative number. So, it is a downward parabola and vertex of a downward parabola represents the maximum value of the function.

It means vertex of the given function represents the maximum height of the ball.

If a quadratic function is defined as

f(x)=ax^2+bx+c

then vertex of the function is

Vertex=(-\frac{b}{2a},f(-\frac{b}{2a}))

In the given function, a=-4.9,b=9.8,c=15.

-\frac{b}{2a}=-\frac{9.8}{2(-4.9)}=1

Substitute t=1 in the given function.

h(1) = -4.9(1)2 + 9.8(1) + 15=19.9

The vertex of the function is (1,19.9).

Therefore, the maximum height of the ball is 19.9 meters after 1 second.

Nezavi [6.7K]3 years ago
4 0
D. the h coordinate of the vertex is the balls maximum height
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