Understanding applications of quadratic functions

Understanding applications of quadratic functions

by Karine Ptak

​Read the text of the example on the right

​The first thing we need to do is to write an equation.

​

​What do we know? Area is equal to the product of the side measurements of the rectangle. How do we determine the measurements of the sides?

Fill in the Blanks

​The correct answer contains 2x+11 (=length) and 2x+6 (=width).

​Please write this down, as you will need it later.

​Let's write the model

Do we agree that area of the outside/larger rectangle - area of the inside/smaller rectangle = area of the frame?

​

​What is the area of the larger rectangle?

Fill in the Blanks

​Please write it down since you will need it.

Please write it down since you will need it.​

Multiple Choice

What is the area of the inside/smaller rectangle? 

• 17

• 34

• 66

​Once again, write it down.

Fill in the Blanks

​If we replace A by its value, we now have the equation

Multiple Choice

The solutions (zeros) to the equation $$4x^2+34x=28$$  are

• x=-2 and x=-11

• x=-9.26 and x=0.76

• (-2,0) and (-11,0)

• (-9.26,0) and (0.76,0)

​Since we are looking for which values of x will make the function = 0, the correct answers are the x-values only.

​x=-9.76 and x=-0.76

​Almost there!

​Watch the video attached to this slide to take a brain break.

​We know have to analyze which of the two solutions make sense for our story...

​Please substitute each value of x, one at a time, in both the length and the width measurements. Here they are again:

​

​f(x)=2x+11 and ​g(x)=2x+6

​

​In other words, calculate f(-9.26), g(-9.26), f(0.76) and g(0.76). What do you notice???

​How do you know you're ready to move on?

​Open the assignment titled "I can create and use a quadratic model". Your submission is as follows:

​1. State how you chose to solve the equation in detail (you may submit a picture of your work)

​2. State which of the two zeros (if any) you would keep as a REASONABLE solution and why. Explain all of that in the context of the problem.