Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation h = -8t 2 + 40t, where h represents the height of the ball above the ground and t represents the time in seconds. The maximum value achieved by the function is represented by the vertex. Use factoring to answer the following: How many seconds does it take the ball to reach its highest point? What ordered pair represents the highest point that the ball reaches as it travels through the air? Hint: because parabolas are symmetric, the vertex of a parabola is halfway between the zeroes of the quadratic

h = -8t² + 40t; This a parabola equation, where h is the y-axis and t is the x-axis

The axis of symmetry is -b/2a = -40/[(2)(-8)] = (-40)/(-16) and t= 2.5
and the highest point reached is : h = -8(2.5)² -40(2.5), h= 50
Te highest point is 50, reached after a time =2.5

The ordered pair highest point is (2.5 , 50)

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lisboa lisboa · Answer 2 · 2021-10-19T11:56:28+02:00

The ball reaches highest point in 2.5 seconds

The ordered pair represents the highest point that the ball reaches as it travels through the air (2.5, 50)

Given :

The ball travels on a parabolic path represented by the equation [tex]h = -8t^2 + 40t[/tex]

The maximum value achieved by the function is represented by the vertex

To find out the vertex we can write the given equation in vertex form

[tex]h=a(x-h)^2+k[/tex]

where (h,k) is the vertex

Lets apply completing the square method to get the vertex form

[tex]h = -8t^2 + 40t\\h = -8(t^2 -5t)\\[/tex]

Take half of coefficient of 't' and square it

Add and subtract it

[tex]h= -8(t^2 -2.5 t+6.25-6.25)\\h=-8(t^2 -2.5 t+6.25)+50\\\\h=-8(t -2.5)^2+50[/tex]

The value of h=2.5 and k=50

The ball reaches highest point in 2.5 seconds

The ordered pair represents the highest point that the ball reaches as it travels through the air (2.5, 50)

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