Lesson 5

1. Lesson 5

1.5. Explore 4

Mathematics 20-1 Module 3

Module 3: Quadratic Functions

Self-Check 2

Model the following situation using a quadratic function, and then use your graphing calculator to find the answer to the problem.

This is a photo of a water fountain spraying water. The fountain is in the shape of a sea serpent. The water is sprayed from the serpent’s mouth.

Hemera/Thinkstock

If the water stream in the photo leaves the sea serpent’s mouth at a height of 1.4 m above the water and rises another 4 m to its maximum height at a horizontal distance of 8 m from the spout, how far from the serpent will the stream hit the water surface? Give your answer to the nearest 0.1 m. What assumptions are you making?

Answer

When inputting negative quantities into your graphing calculator, be sure to press the negative key, not the subtraction key. The subtraction key is only for finding the difference between two terms.

Also, place the negative number in brackets if the number is squared or raised to a power. For example, (−2)2 = (−2)(−2) = +4, but −22 = −(2)(2) = −4.

Example 2: From the Textbook

Take a look at modelling a different type of problem. Study “Example 4” on pages 190 to 191 in the textbook. Take note of how to set up and solve the problem with and without a graphing calculator.

Self-Check 3

A hobby rancher has 200 m of fencing and wants to construct two adjoining pastures of equal size. His plan is that horses can graze one pasture while the grass in the other pasture grows back, at which time the horses will switch pastures. What are the dimensions of the pastures that will give the maximum area?

Answer

This is a sketch of the pasture and fence.

If you feel you have a solid understanding of how to model a situation using a quadratic function and how to use a graphing calculator, go to Connect. If you feel you need a bit more practice, complete Self-Check 4.

Self-Check 4

Complete questions 15, 17, 18, 21, and 22 on pages 194 to 196 in the textbook. Check your work in the back of the textbook. If you are still unclear about how to answer some questions, contact your teacher.

Step 1: Draw a diagram showing the pastures.

Step 2: Write an equation for in terms of w and the amount of fencing available.

Step 3: Write an equation for the area of the pastures.

Step 4: Find the maximum value for the area using your function.

You might want to break the problem into steps as was done in Example 1: Water Stream.

If you make the origin at the serpent’s mouth, the y-value where the stream hits the water surface will be y = −1.4.

If you make the origin at the serpent’s mouth, the coordinates of the vertex are (8, 4).