Question

A golf ball is hit off a tee toward the green. The height of the ball is modeled by the function h(t) = −16t2 + 96t, 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?

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.
t = 3; It takes the ball 3 seconds to reach the maximum height and 3 seconds to fall back to the ground.
t = 6; It takes the ball 6 seconds to reach the maximum height and 3 seconds to fall back to the ground.
t = 6; It takes the ball 6 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Answer 1

Answer:

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground

Step-by-step explanation:

we have

$h(t)=-16t^2+96t$

This is a vertical parabola open downward

The vertex represent a maximum

where

t represent the time in seconds

h(t) represent the height of the ball

What is the axis of symmetry, and what does it represent?

we know that

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

Convert the quadratic equation into vertex form

$h(t)=-16t^2+96t$

step 1

Factor -16

$h(t)=-16(t^2-6t)$

step 2

Complete the square

$h(t)=-16(t^2-6t+9)+144$

step 3

Rewrite as perfect squares

$h(t)=-16(t-3)^2+144$

The vertex is the point (3,144)

That means ----> It takes the ball 3 seconds to reach the maximum height of  144 units

The x-coordinate of the vertex is 3

therefore

The equation of the axis of symmetry is

$x=3$

step 4

Find how long take to the ball hit the ground

we know that

When the ball hit the ground the height is equal to zero

so

For h(t)=0

$-16(t-3)^2+144=0$

Solve for t

$16(t-3)^2=144$

$(t-3)^2=\frac{144}{16}$

take square root both sides

$(t-3)=\pm3$

$t=\pm3+3$

so

$t=+3+3=6\ sec$

$t=+3-3=0\ sec$

therefore

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground

Answer 2

Answer:

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground

Step-by-step explanation:

we have

This is a vertical parabola open downward

The vertex represent a maximum

where

t represent the time in seconds

h(t) represent the height of the ball

What is the axis of symmetry, and what does it represent?

we know that

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

Convert the quadratic equation into vertex form

step 1

Factor -16

step 2

Complete the square

step 3

Rewrite as perfect squares

The vertex is the point (3,144)

That means ----> It takes the ball 3 seconds to reach the maximum height of  144 units

The x-coordinate of the vertex is 3

therefore

The equation of the axis of symmetry is

step 4

Find how long take to the ball hit the ground

we know that

When the ball hit the ground the height is equal to zero

so

For h(t)=0

Solve for t

take square root both sides

so

therefore

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground