3.2 Writing Quadratics with Word Problems

3.2 Writing Quadratics to Represent the Real World

Steps to Write a Quadratic From a Word Problem

• Read the scenario and underline details

• Sketch the parabola and key details

• Were you provided the vertex and a point? Three points on the parabola? Use these to write a function

• Graph to check and remember to apply reason - a ball cannot land underground, time cannot go backwards or negative, etc.

Read the example then continue to watch the video.

Dylan shoots an arrow from an initial height of 2 meters. The arrow reaches its maximum height of 20 meters after it has flown 60 meters away. Write a quadratic function to represent the height of the arrow as a function of distance.

Multiple Choice

A basketball player stands near the middle of the court and throws the ball toward the basket. The path of the ball is a parabola. The ball leaves the player’s hands at a height of 6 feet above the ground. The ball travels to a maximum height of 12 feet when it is a horizontal distance of 18 feet from the player’s hands. Write a function to represent the height of the ball in terms of its distance from the player’s hands.

• $y=-\frac{1}{54}\left(x-18\right)^2+12$

• $y=\frac{1}{54}\left(x+18\right)^2+12$
  

• $y=-\frac{1}{54}\left(x-6\right)^2$

•  $y=-\frac{1}{54}\left(x-12\right)^2+18$ 

Poll

How did that go? Select all that apply and be honest with yourself.

• I got it right!

• I got it wrong.

• I guessed...?

Lets look at another one together. Read the example then continue to watch the video.

Patricio stands on a small hill and kicks a soccer ball to the ground below. The hill is 6 feet above the ground. The path of the ball is a parabola. When the ball is a horizontal distance of 12 feet from him, it is 14 feet above the ground. When the ball is horizontal distance of 32 feet from him it is 7 feet above the ground. Write a function for the height of the ball in terms of its horizontal distance. Round to the nearest thousandth.

Multiple Choice

Jamal and Cedric were playing football in the front yard. Cedric kicked the ball over the rooftop and it landed in the backyard. The ball was on the ground when Cedric kicked it and reached a height of 20 ft after 1 second. The ball hit the ground in the backyard after 5 seconds. Write the function h, height of the ball with respect to the time t. Find the height of the ball at 4 seconds.

What are you given?

• Vertex and a Point

• 3 Points

Multiple Choice

Jamal and Cedric were playing football in the front yard. Cedric kicked the ball over the rooftop and it landed in the backyard. The ball was on the ground when Cedric kicked it and reached a height of 20 ft after 1 second. The ball hit the ground in the backyard after 5 seconds. Write the function h, height of the ball with respect to the time t. Find the height of the ball at 4 seconds.

What is the equation?

• $h=5t^2+25t+1$

•  $t=-5h^2+25h$ 

•  $h=-5t^2+25t$ 

• Not possible

Multiple Choice

Jamal and Cedric were playing football in the front yard. Cedric kicked the ball over the rooftop and it landed in the backyard. The ball was on the ground when Cedric kicked it and reached a height of 20 ft after 1 second. The ball hit the ground in the backyard after 5 seconds. Write the function h, height of the ball with respect to the time t. Find the height of the ball at 4 seconds.

What is the height at 4 seconds?

• 10 feet

• 20 feet

• 30 feet

• Not possible

This is for a grade! You must make a 70 on this lesson to receive credit.

At the end of the unit, I will see what lessons you have completed. If you completed all of them, it's an easy 100 for a quiz.