Home Run Quadratics

Home Run Quadratics Activity

You'll want a piece of paper for scratch work

Multiple Choice

Review:
What is the vertex?

 $y=-\left(x+5\right)^2-1$  

• (-5, 1)

• (-5, -1)

• (5, -1)

• (5, 1)

Multiple Choice

Review:
What is the maximum value?

 $y=-16\left(x-3\right)^2+27$  

• 24

• 16

• 3

• 27

The left field wall in Boston’s Fenway Park – aka Green Monster – is 310 feet from home plate and 37 feet tall.  

In this activity, x represents distance from home plate and y represents height.

Instead of x, d will be used to represent distance.

All measurements are in feet.

Multiple Choice

Suppose a batter hit the ball. The trajectory of the ball is

 $y=-0.08\left(d-49\right)^2+195$ 

What does d represent?

• time in seconds

• height

• distance from home plate

Multiple Choice

Suppose a batter hit the ball. The trajectory of the ball is

 $y=-0.08\left(d-49\right)^2+195$ 

What does y represent?

• time in seconds

• height of the ball

• distance from home plate

Multiple Choice

Suppose a batter hit the ball. The trajectory of the ball is

 $y=-0.08\left(d-49\right)^2+195$ 

What is the maximum height of the ball? 

• 195 feet

• 49 feet

• 80 feet

• 146 feet

Multiple Choice

Suppose a batter hit the ball. The trajectory of the ball is

 $y=-0.08\left(d-49\right)^2+195$ 

How far is the ball from home plate when it reaches its maximum height?

• 195 feet

• 49 feet

• 80 feet

• 146 feet

Multiple Choice

Suppose a batter hit the ball. The trajectory of the ball is

 $y=-0.08\left(d-49\right)^2+195$ 

In this scenario, what do you think the y-intercept represents?

• The time it took the ball to land

• The maximum height of the ball

• Total distance the ball traveled

• The height of the ball when the batter makes contact with it

Multiple Choice

Suppose a batter hit the ball. The trajectory of the ball is

 $y=-0.08\left(d-49\right)^2+195$ 

Find the y-intercept (height at contact) by setting d=0.

• 2.92 feet

• 8 feet

• 0.08 feet

• 3.87 feet

Multiple Choice

Suppose a batter hit the ball. The trajectory of the ball is

 $y=-0.08\left(d-49\right)^2+195$ 

In this scenario, what do you think the x-intercept represents?

• The time it took the ball to land

• The maximum height of the ball

• Total distance the ball traveled

• The height of the ball when the batter makes contact with it

Multiple Choice

Suppose a batter hit the ball. The trajectory of the ball is

 $y=-0.08\left(d-49\right)^2+195$ 

Find the x-intercept (total distance the ball traveled) by setting y=0.

• 2.92 feet

• 64.61 feet

• 98.37 feet

• 3.87 feet

Multiple Choice

Remember, the left field wall in Boston’s Fenway Park – aka Green Monster – is 310 feet from home plate and 37 feet tall.  

 $y=-0.08\left(d-49\right)^2+195$ 

Would the hit in the previous problems make it over the wall for a home run?

• no

• yes

We found that the ball will only travel approximately 98 feet from home plate, which means it does not make it far enough to be a home run.

Multiple Choice

Someone else is up to bat now.  The trajectory of their ball is

 $y=-0.0002\left(d-182\right)^2+10$ 

What is the maximum height of the ball? 

• 182 feet

• 20 feet

• 10 feet

• 172 feet

Multiple Choice

Someone else is up to bat now.  The trajectory of their ball is

 $y=-0.0002\left(d-182\right)^2+10$ 

How far is the ball from home plate when it reaches its maximum height?

• 182 feet

• 20 feet

• 10 feet

• 172 feet

Multiple Choice

Someone else is up to bat now.  The trajectory of their ball is

 $y=-0.0002\left(d-182\right)^2+10$ 

Find the y-intercept (height at contact).

• 2.86 feet

• 16.625 feet

• 55.25 feet

• 3.375 feet

Multiple Choice

Someone else is up to bat now.  The trajectory of their ball is

 $y=-0.0002\left(d-182\right)^2+10$ 

Find the x-intercept (total distance the ball traveled).

• 662.48 feet

• 16.625 feet

• 405.6 feet

• 252.7 feet

Multiple Choice

Remember, the left field wall in Boston’s Fenway Park – aka Green Monster – is 310 feet from home plate and 37 feet tall.  

 $y=-0.0002\left(d-182\right)^2+10$ 

Would the hit in the previous problems make it over the wall for a home run?

• no

• yes

This ball had the distance but never made it higher than 10 feet.

The ball's max. height is only 10 feet so it would not be a home run.

Multiple Choice

A third batter is up to the plate.  The trajectory of their ball is

 $y=-0.004\left(d-173\right)^2+123$ 

What is the maximum height of the ball? 

• 40 feet

• 123 feet

• 173 feet

• 50 feet

Multiple Choice

A third batter is up to the plate.  The trajectory of their ball is

 $y=-0.004\left(d-173\right)^2+123$ 

How far is the ball from home plate when it reaches its maximum height?

• 40 feet

• 123 feet

• 173 feet

• 50 feet

Multiple Choice

A third batter is up to the plate.  The trajectory of their ball is

 $y=-0.004\left(d-173\right)^2+123$ 

Find the y-intercept (height at contact).

• 3.28 feet

• 2.94 feet

• 111.03 feet

• 4.07 feet

Multiple Choice

A third batter is up to the plate.  The trajectory of their ball is

 $y=-0.004\left(d-173\right)^2+123$ 

Find the x-intercept (total distance the ball traveled).

• 348.36 feet

• 381.53 feet

• 111.03 feet

• 207.84 feet

Multiple Choice

Remember, the left field wall in Boston’s Fenway Park – aka Green Monster – is 310 feet from home plate and 37 feet tall.  

 $y=-0.004\left(d-173\right)^2+123$ 

Would the hit in the previous problems make it over the wall for a home run?

• no

• yes

Poll

I hope I hit this assignment out of the park for you.

• I am completely lost.

• That was fun.

• That was lame.

• I'm indifferent.