1. Lesson 3

1.5. Explore

Mathematics 20-1 Module 3

Module 3: Quadratic Functions

 

Explore

 

It is often easier to model problems using the standard form of the quadratic function, y = ax2 + bx + c; however, it is easier to draw a graph and find minimum or maximum values from the vertex form, y = a(x − p)2 + q. This is why you are learning to convert quadratic functions from the standard form to the vertex form.

course folder Save Module 3 Glossary Terms in your course folder now.



glossary

Here are some of the words you will want to define in Module 3 Glossary Terms in this lesson:

  • standard form of the quadratic equation
  • vertex form of the quadratic equation
  • binomial
  • trinomial
  • polynomial
  • coefficient
Try This 2

 

In Try This 1 you used algebra tiles to complete the square for a trinomial in the form ax2 + bx + c. The first quadratic function in the table, x2 + 2x − 8, was shown to equal the sum of the perfect-square trinomial and the leftover term.

 

 

Quadratic Function

Perfect-Square Trinomial

Leftover Term

x2 + 2x − 8

x2 + 2x + 1

 

This illustration shows a square of side (x + 1).

− 9

 

This illustration shows nine negative-one tiles.
  1. Factor the perfect-square trinomial. hint

  2. Write the quadratic in the new form: x2 + 2x − 8 = (square of a binomial) + (leftover term).

  3. How does this form compare with the vertex form, y = a(x − p)2 + q, of a quadratic function?

  4. Rewrite two more quadratics from the chart in Try This 1 in the vertex form using this method.

course folder Save your responses in your course folder.

This step is important to getting the next two questions right. Did you get this: x2 + 2x + 1 = (x − 1)2?