Lesson 3
1. Lesson 3
1.5. Explore
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.
Save Module 3 Glossary Terms in your course folder now.
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
|
− 9
|
- Factor the perfect-square trinomial.
- Write the quadratic in the new form: x2 + 2x − 8 = (square of a binomial) + (leftover term).
- How does this form compare with the vertex form, y = a(x − p)2 + q, of a quadratic function?
- Rewrite two more quadratics from the chart in Try This 1 in the vertex form using this method.
Save your responses in your course folder.