In this lesson, you will determine what expressions would produce graphs with particular vertices. We will 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.

When you finish this lesson, you will be able to:

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

Here are the activities that will help you reach those goals:

• 7.17.1: Quadratic Expressions in Different Forms
• 7.17.2: Modify Expressions to Translate Graphs
  • 7.17.2: Self Check
  • 7.17.2: Additional Resources
• 7.17.3: Changing the Parameters of a Quadratic Expression
  • 7.17.3: Self Check
  • 7.17.3: Additional Resources
• 7.17.4: Transforming the Parent Function
• 7.17.5: Equations of Graph Translations

After that, you’ll practice and review.

• 7.17.6: Practice
• 7.17.7: Lesson Summary