Cogito
Algebra 1 · Chapter 8 · Lesson 4
The Vertex and Axis of Symmetry
The turning point, and the mirror through it.
11 problems · about 23 minutes · F-IF.C.8, F-IF.B.4
What this lesson teaches
The student finds the vertex and axis of symmetry of a parabola.
- The axis of symmetry is x = −b / 2a, and the vertex sits on it.
- A positive a gives a minimum; a negative a gives a maximum.
- The axis is halfway between the roots whenever they exist.
Warm Up
Straightforward practice. Get the method working first.
4 problemsy = x² − 10x + 2. Axis of symmetry, as an x value?
Answer 5
Why x = 5.
y = x² − 4x + 1. Axis of symmetry, as an x value?
Answer 2
Why 4 ÷ 2.
y = x² − 4x + 1. What is the y of the vertex?
Answer -3
Why 4 − 8 + 1.
y = x² + 6x. Axis of symmetry, as an x value?
Answer -3
Why −6 ÷ 2.
Build It Up
The same ideas with more to keep track of.
3 problemsRoots at 2 and 8. Where is the axis of symmetry?
Answer 5
Why Halfway between.
a = 3. Is the vertex a minimum? 1 for yes, 0 for no.
Answer 1
Why It opens upward.
y = x². Where is the vertex, as an x value?
Answer 0
Why At the origin.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsRoots at −4 and 6. Where is the axis of symmetry?
Answer 1
Why Halfway between.
Select every true statement about the vertex.
Answer It lies on the axis of symmetry.; Its x is −b / 2a.
Why The sign of a decides maximum or minimum.
The Axis: y = x² − 8x + 1. What is the axis of symmetry, as an x value?
Answer 4
Why x = 4.
Max or Min: y = −x² + 4x. Is the vertex a maximum? 1 for yes, 0 for no.
Answer 1
Why Maximum.