Graphing from the Vertex Form

5 min

Narrative

This Warm-up highlights the three forms of quadratic expressions that students have seen so far. It reinforces how each form gives different insights into the graph of a quadratic function.

Launch

Arrange students in groups of 2. Give students a minute of quiet think time, and then ask them to share their thinking with a partner.

Student Task

Expressions in different forms can be used to define the same function. Here are three ways to define a function, ff.

f(x)=x2−4x+3f(x)=x^2-4x+3

standard form

f(x)=(x−3)(x−1)f(x)=(x-3)(x-1)

factored form

f(x)=(x−2)2−1f(x)=(x-2)^2-1

vertex form

Which form would you use if you want to find the following features of the graph of ff? Be prepared to explain your reasoning.

  1. the xx-intercepts
  2. the vertex
  3. the yy-intercept

Sample Response

  1. factored form
  2. vertex form
  3. In standard form we can see that the graph intersects the yy-axis at 3, but in any form, we can pretty easily find the output when the input is 0.

Synthesis

Invite students to share their responses and explanations. Encourage students to name specific features of the graph of ff. If time permits, consider asking students to use all of the information they can gather to sketch a graph.

If not already mentioned by students, point out that while the standard form allows us to find the yy-intercept more readily, the yy-intercept can always be found by evaluating the function at x=0x=0.

Standards
Addressing
  • F-IF.C·Analyze functions using different representations
  • HSF-IF.C·Analyze functions using different representations.

20 min

10 min