Understanding Quadratic Functions and Graphs

This video tutorial explains how to plot quadratic functions on a graph. It begins with an introduction to quadratic functions, highlighting their U or N shapes based on the sign of the x² term. The tutorial then guides viewers through plotting a quadratic function using a table of values, demonstrating the substitution and calculation of coordinates. It emphasizes the importance of careful calculation, especially with negative numbers, and provides tips for graphing, such as using a pencil for corrections and ensuring the graph is symmetrical. The video concludes with advice on adjusting x-coordinates for a better fit on the graph.

What is the shape of a quadratic function with a positive x² term?

• U-shaped

• Linear

• N-shaped

• Circular

How can you identify a quadratic function?

• By its highest power being x²

• By its linearity

• By its constant term

• By its cubic term

What is the shape of the graph for the equation y = -x²?

• Linear

• N-shaped

• Exponential

• U-shaped

In the equation y = 0.5x² + 6, what does the 0.5 indicate about the graph's shape?

• It will be circular

• It will be linear

• It will be N-shaped

• It will be U-shaped

What should you do if you make a mistake while plotting the graph?

• Use a pen to correct it

• Ignore it

• Erase and start again

• Start a new graph

Why is it important to label the curve with the equation?

• To identify the graph

• To make it look neat

• To make it colorful

• To confuse others

How many coordinates are typically needed to plot a quadratic graph?

• At least 10

• At least 7

• At least 5

• At least 3

What should you do if some x-coordinates do not fit on the graph?

• Change the equation

• Use a larger graph

• Choose different x-coordinates

• Ignore them

What is a common mistake when calculating y-values for a quadratic function?

• Forgetting to square x

• Multiplying negatives incorrectly

• Adding instead of subtracting

• Using the wrong formula

What is a useful tool for completing the table of values easily?

• A compass

• A protractor

• A ruler

• A calculator trick