Example: Graphing y=-cos(π⋅x)+1.5 | Trigonometry | Algebra 2 | Khan Academy

TL;DR

The video demonstrates how to graph the equation y = -cos(pi*x) + 1.5, showing step-by-step transformations.

Transcript

• [Instructor] We're told to graph y is equal to negative cosine of pi times x plus 1.5 in the interactive widget. So, pause this video and think about how you would do that. And just to explain how this widget works if you're trying to do it on Khan Academy, this dot right over here helps define the midline. You can move that up and down. And then... Read More

Key Insights

• 😥 The interactive widget on Khan Academy allows users to manipulate the midline and extreme points for graphing functions.
• ➕ The negative sign in y = -cos(pi*x) flips the function vertically, while the plus 1.5 shifts it upward.
• 🗂️ The period of the graph is determined by dividing 2*pi by the coefficient of x.
• 😥 The manipulation of points helps to achieve the desired period and shape of the graph.
• 😀 The graph of y = -cos(pi*x) + 1.5 exhibits oscillation above and below the midline.
• 👶 The addition of 1.5 to the graph shifts it vertically, resulting in a new midline.
• ❓ Understanding the effects of each component enables accurate graphing of the equation.

Questions & Answers

Q: How do you graph the equation y = -cos(pi*x) + 1.5?

To graph the equation, you need to understand the effects of each component. Start by graphing the cosine function, then flip it with the negative sign, and finally shift the graph up by 1.5 units.

Q: What happens when x is equal to zero in the equation y = -cos(pi*x) + 1.5?

When x is equal to zero, the cosine of pi times zero is equal to one. However, the negative sign flips it to -1. When you add 1.5, the result is 0.5.

Q: How do you determine the period of the graph?

For the cosine function of the form cos(pix), the period is found by dividing 2pi by the coefficient of x. In this case, the period is 2.

Q: Why is the midline point manipulated in the graphing process?

By manipulating the midline point, you can ensure that the maximum point occurs at x = 0, which aligns with the cosine function. This helps set the correct period and shape of the graph.

Summary & Key Takeaways

• The video explains how to graph the equation y = -cos(pi*x) + 1.5 using an interactive widget on Khan Academy.

• Step-by-step instructions are given for transforming the cosine function, including understanding the effects of the negative sign and the plus 1.5.

• The graphing process involves manipulating the midline and extreme points to achieve the desired period and shape of the graph.