Cogito
Integrated Math 2 · Chapter 1 · Lesson 1
Graphs of Quadratic Functions
The parabola and its features.
12 problems · about 21 minutes · F-IF.C.7, F-IF.B.4
What this lesson teaches
The student identifies the vertex, axis of symmetry and intercepts of a parabola.
- A quadratic graphs as a symmetric parabola.
- The vertex sits at x = −b ÷ 2a, and c is the y-intercept.
- The sign of a decides the direction; its size decides the width.
Warm Up
Straightforward practice. Get the method working first.
5 problemsy = x² − 8x + 1. What is the vertex x-coordinate?
Answer 4
Why 4.
What does a negative leading coefficient mean?
Answer The parabola opens downward and has a maximum.
Why Downward, with a maximum at the vertex.
y = x² − 6x + 5. Vertex x-coordinate?
Answer 3
Why 6 ÷ 2.
y = 2x² + 8x. Vertex x-coordinate?
Answer -2
Why −8 ÷ 4.
y = −x² + 4. Does it open up or down? 1 up, 2 down.
Answer 2
Why Negative leading coefficient.
Build It Up
The same ideas with more to keep track of.
3 problemsy = 3x² − 12x + 7. What is the y-intercept?
Answer 7
Why The constant.
y = x² − 6x + 5 at x = 3. What is y?
Answer -4
Why 9 − 18 + 5.
A parabola opening upward has a maximum or minimum? 1 maximum, 2 minimum.
Answer 2
Why The vertex is the lowest point.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each coefficient by what it controls.
Answer Direction and width: The sign of a, The size of a · Position on the grid: The value of c, The value of b
Why Only a decides which way it opens and how narrow it is.
y = x² − 10x + 2. Vertex x-coordinate?
Answer 5
Why 10 ÷ 2.
The Turning Point: y = x² − 4x + 3. What is the x-coordinate of the vertex?
Answer 2
Why 2.
The Intercept: y = x² − 4x + 3. What is the y-intercept?
Answer 3
Why 3.