Activity
Your teacher will give your group a set of cards. 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.
Once all the cards are sorted and discussed, record the equivalent equations, sketch the corresponding graph, and write a brief note or explanation about why the representations were grouped together.
Compare your answer:
Set 1: Standard Form: Factored Form:
Set 2: Standard Form: Factored Form:
Set 3: Standard Form: Factored Form:
Set 4: Standard Form: Factored Form:
Self Check
Additional Resources
Matching Quadratic Functions and Their Graphs
Below is a quadratic function represented in standard form, factored form, and with a graph.
Standard Form:
Factored Form:
Notice the factored form helps find the zeros: and .
The factored form gives the zeros since the zeros (-intercepts) are located where each factor equals 0.
The standard form, , helps give the -intercept. The -intercept occurs when . Here, . On the graph, the -intercept is .
Try it
Try It: Matching Quadratic Functions and Their Graphs
Given the graph below and its function in standard form and factored form, identify all intercepts.
Standard form: Factored form:
Here is how to find the intercepts with the information provided:
The graph and the factored form help give the -intercepts. They occur where the factors of the factored form equal 0, at and . On the graph, these are where the graph crosses the -axis, at the points and .
The -intercept can be found with standard form when in . So . Notice on the graph, the -intercept, where the graph crosses the -axis, is at .