# Lesson 17

Changing the Vertex

### Lesson Narrative

Previously, students were given quadratic expressions in vertex form and asked to visualize the location of the vertex and the direction of the opening of the graph representing each expression. In this lesson, they reason the other way around and think about what expressions would produce graphs with particular vertices. Students look more closely at how changing the $$h$$ and the $$k$$ in a quadratic expression of the form $$a(x-h)^2 +k$$ translates the graph, and recall that the coefficient $$a$$ affects the direction of the opening of a parabola.

Students continue to reason abstractly with expressions and graphs, but in one of the activities they also reconnect abstract expressions and quantities to a context. They continue to consolidate the ideas, structure, and generalizations from the past few lessons and apply them in new ways (MP7).

### Learning Goals

Teacher Facing

• Create a quadratic function by changing the vertex of an existing function given its equation, graph, and a description.
• Describe informally (orally and in writing) the effect on the graph of a quadratic function when performing simple algebraic transformations.

### Student Facing

• Let’s write new quadratic equations in vertex form to produce certain graphs.

### Required Preparation

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.)

Devices are required for the digital version of the activity "A Peanut Jumping over a Wall." Be prepared to display an applet for all to see during the activity synthesis.

### Student Facing

• I can describe how changing a number in the vertex form of a quadratic function affects its graph.

### Glossary Entries

• 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.