IM Alg1.6.12 Lesson: Graphing the Standard Form (Part 1)
Graphs A, B, and C represent 3 linear equations:
, , and
Which graph corresponds to which equation? Explain your reasoning.
Graph y=x² and then experiment with each of the following changes to the function. Record your observations (include sketches, if helpful).
Adding different constant terms to (for example: , , , etc.)
Multiplying by different positive coefficients greater than 1 (for example: , , etc.)
Multiplying by different negative coefficients less than or equal to -1 (for example: , , etc.)
Multiplying by different coefficients between -1 and 1 (for example: , , etc.)
Here are the graphs of three quadratic functions.
What can you say about the coefficients of in the expressions that define (in black at the top)?
What can you say about the coefficients of in the expressions that define (in blue in the middle)?
What can you say about the coefficients of in the expressions that define (in yellow at the bottom)?
Can you identify them? How do they compare?
Earlier, you observed the effects on the graph of adding or subtracting a constant term from . Study the values in the table. Use them to explain why the graphs changed the way they did when a constant term is added or subtracted.
You also observed the effects on the graph of multiplying by different coefficients. Study the values in the table. Use them to explain why the graphs changed they way they did when is multiplied by a number greater than 1, by a negative number less than or equal to -1, and by numbers between -1 and 1.
Each card contains a graph or an equation.
- Take turns with your partner to sort the cards into sets so that each set contains two equations and a graph that all represent the same quadratic function.
- For each set of cards that you put together, explain to your partner how you know they belong together.
- For each set that your partner puts together, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.