Cogito
Algebra 1 · Chapter 8 · Lesson 1
Parabolas and Their Roots
What the graph tells you about the solutions.
10 problems · about 20 minutes · F-IF.C.7, A-REI.B.4, A-APR.B.3
What this lesson teaches
The student graphs quadratic functions and relates the roots to the x-intercepts.
- A quadratic graphs as a parabola.
- Its roots are where the graph crosses the x-axis.
- The vertex sits at x = −b ÷ 2a.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Factoring Quadratic Trinomials: Multiply to 18, add to 9. Larger number?
Answer 6
Why 6.
Review — Multiplying and Factoring: x² + 11x + 24 = (x + 3)(x + ?). Missing number?
Answer 8
Why 8.
Warm Up
Straightforward practice. Get the method working first.
4 problemsx² − 7x + 12 = 0. What is the larger root?
Answer 4
Why x = 4.
What do the roots of a quadratic correspond to on its graph?
Answer Where it crosses the x-axis.
Why The x-intercepts.
x² − 9 = 0. What is the positive root?
Answer 3
Why Difference of squares.
(x − 1)(x − 6) = 0. What is the larger root?
Answer 6
Why Set each factor to zero.
Build It Up
The same ideas with more to keep track of.
2 problemsy = x² − 8x + 3. x-coordinate of the vertex?
Answer 4
Why 8 ÷ 2.
x² + 5x + 6 = 0. What is the larger root?
Answer -2
Why (x + 2)(x + 3).
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Roots: (x − 4)(x − 7) = 0. What is the larger root?
Answer 7
Why x = 7.
The Vertex: y = x² − 6x + 5. What is the x-coordinate of the vertex?
Answer 3
Why x = 3.