Lesson 9
1. Lesson 9
1.3. Explore 3
Module 3: Quadratics
The answer you obtained in Self-Check 1 is the same as the answer obtained by placing the origin at the vertex. Which method do you prefer?
When modelling a problem, choose a position for the origin that simplifies the amount of computation required. Putting the origin at the vertex, at a point under the vertex, or at one of the endpoints of the parabola often works well.
The choice of whether to use the standard form or the vertex form of the quadratic function depends on the values you know from the situation. As you have seen, either form will give you the same final answer.
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Self-Check 2
In this activity you will model a situation using a quadratic function; then you will use a graphing calculator or the quadratic formula to find the answer to a related problem.
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’s surface? Give your answer to the nearest 0.1 m. What assumptions are you making?
If you get stuck, consider the following hints:
- If you choose the origin to be at the serpent’s mouth, the coordinates of the vertex are (8, 4).
- If you choose the origin to be at the serpent’s mouth, the y-value where the stream hits the water’s surface will be y = −1.4.
When inputting negative quantities into your graphing calculator, be sure to press the negative key, (−), located directly left of the ENTER key. The negative key on the calculator is a subtraction symbol enclosed in a parentheses. Use the subtraction key, −, located two spaces above the ENTER key only for the subtraction operation of finding the difference between two terms.
Take a look at modelling a different type of problem. In your textbook, study “Example 3: Solving a problem by creating a quadratic model” and “Example 4: Visualizing a quadratic relationship” on pages 428 and 429. You will see how to set up and solve a problem with and without a graphing calculator.
If you haven’t done so already, you may want to add what you’ve learned about creating equations to help solve problems to your notes organizer.
If you feel you need a bit more practice, complete Self-Check 3 before moving to Connect.
Self-Check 3
Complete all or parts of questions 3, 5, 7, and 8 from on pages 430 and 431 of the textbook. When you finish a question, check your work using the shortened answers given on page 566 of the textbook. If you are still unclear about how to answer some questions, ask your teacher for help.