This lesson is optional because it goes beyond the depth of understanding required to address the standards. In this lesson, students continue to examine the ties between quadratic expressions in standard form and the graphs that represent them. The focus this time is on the coefficient of the linear term, the \(b\) in \(ax^2+bx+c\), and how changes to it affect the graph. Students are not expected to know how to modify given expressions to transform the graphs in certain ways, but they will notice that adding a linear term to the squared term translates the graph in both horizontal and vertical directions. This understanding will help students to conclude that writing an expression such as \(x^2+bx\) in factored form can help us reason about the graph.
Students also practice writing expressions that produce particular graphs. To do so, students make use of the structure in quadratic expressions (MP7) and what they learned about the connections between expressions and graphs.
- Describe (orally and in writing) how the $b$ in $y=ax^2+bx+c$ affects the graph.
- Write quadratic expressions in standard and factored forms that match given graphs.
- Let’s change some other parts of a quadratic expression and see how they affect the graph.
Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)
- I can explain how the $b$ in $y=ax^2+bx+c$ affects the graph of the equation.
- I can match equations given in standard and factored form with their graph.