In earlier lessons, students have determined the \(x\)-coordinate of the vertex of a graph by determining the value exactly between the two \(x\)-intercepts. They have seen that the vertex of a graph that represents a quadratic function tells us the maximum or minimum value of the function. Because of this, we are often interested in identifying the vertex of a graph. In this lesson, students are introduced to quadratic expressions in vertex form and learn that this form allows us to easily see where the vertex of a graph is.
Students use technology to experiment with the parameters of expressions in vertex form, examine how they are visible on the graphs, and articulate their observations, all of which require attending to precision (MP6). They also consider how the connections between expressions and graphs here are like or unlike other connections they studied in earlier lessons.
- Comprehend quadratic expressions in “vertex form” by seeing the form as a constant plus a coefficient times a squared term.
- Coordinate (using words and other representations) the parameters of a quadratic expression in vertex form and the graph that represents it.
- Let’s find out about the vertex form.
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 recognize the “vertex form” of a quadratic equation.
- I can relate the numbers in the vertex form of a quadratic equation to its graph.
vertex form (of a quadratic expression)
The vertex form of a quadratic expression in \(x\) is \(a(x-h)^2 + k\), where \(a\), \(h\), and \(k\) are constants, and \(a\) is not 0.