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A football is kicked towards the goal. The height of the ball is modeled by the function H(t)=-16t^2+64t where T equals the time in seconds and H(t) represents the height of the ball at time T seconds. What is the axis of symmetry and what does it represent?

Respuesta :

Edufirst
The function H(t) = -16t^2 + 64t is a parabola.

The axis of symmetry of a parabola is at the midpoint between the two real roots.

The roots are the solutions of H(t) = 0

Then find the roots:

-16t^2 + 64t = 0

Factor => t(-16t + 64) = 0 => t = 0 and -16t + 64 =0

-16t + 64 = 0 => t = 64 / 16 = 4

Then the two roots are t = 0 and t = 4, and the axis of symmetry is t = (0 + 4) / 2 = 4/2 = 2

Answer:

The axis of simmetry is t = 2.

It represents the time at which the ball is at the higher point, i.e the maximum height.

You can find the maximum height replacing t = 2 in the function H(t)

H(t) = -16(2^2) + 64(2) = 64 feet.

And you can also deduce that the second part of the flight will take 2 seconds, for a total flight time of 4 seconds.


 

The axis of the symmetry of a parabola is a vertical line that divides the parabola in two equal parts. The axis of the symmetry is 2 which represents that the maximum height (64 units) reached by the ball is after two seconds.

Given information-

The height of the ball is modeled with the function,

[tex]H(t)=-16t^2+64t[/tex]

Here t is the time in seconds.

Axis of symmetry

The axis of the symmetry of a parabola is a vertical line that divides the parabola in two equal parts.

As the roots of the parabola divides it into the two equal part. Therefore equate the equation to the 0 for finding the roots of the equation.

[tex]-16t^2+64t=0\\ -16t(t-4)=0[/tex]

Thus one roots of the equation are,

[tex]\begin{aligned}\\ -16t&=0\\ t&=0\\ \end[/tex]

Another root,

[tex]\begin{aligned}\\ t-4&=0\\ t&=4\\ \end[/tex]

The roots of the equation are (0,4). The axis of the parabola is the half of the sum of the roots of the equation of that parabola,

[tex]t=\dfrac{0+4}{2} \\ t=2[/tex]

Put this value of t in the given equation to find the height.

[tex]H(t)=-16\times2^2+64\times2\\ H(t)=-64+128\\ H(t)=64[/tex]

Hence the axis of the symmetry is 2 which represents that the maximum height (64 units) reached by the ball is after two seconds.

Learn more about the axis of symmetry here;

https://brainly.com/question/21589886

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