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The Axis of Symmetry

Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 1 of 48.

A ball leaves your hand 1 m up. It is 1 m up again 4 seconds later. Its path is a parabola, a U-shaped curve with a mirror line. It is highest halfway, at 2 seconds. $y = {ax}^{2}+bx+c$ has height c at x = 0 and at $x = \frac{-b}{a}$ . The mirror line, the axis of symmetry, is halfway: $x = \frac{-b}{2a}$ .

$A parabola opening down through (0, 1) and (4, 1), with a dashed vertical line at x = 2$

Challenge

Where is the mirror line of $f\left(x\right) = 3{x}^{2}-18x+4$ ? On the first line, write $h = ...$ with a and b put into $\frac{-b}{2a}$ . On the second line, write the value of h.

Start the lesson to read it in the interactive player and track your progress.

All lessons in Quadratics & Complex Numbers

1The Vertex

The Axis of SymmetryDrawing from Standard Form Maximum or Minimum Recap: The Vertex

4Imaginary Numbers

Meet i Roots of Negatives Not a Perfect Square Powers of i Recap: Imaginary Numbers

7The Discriminant

Computing It Three Kinds of Answers Reading the Sign Recap: The Discriminant

10Final Challenges

Final: Square It Away Final: The Peak Final: Divide It Final: No Real Roots Final: Where They Meet

2Completing the Square

The Missing Number Completing the Square When a Is Not 1 Recap: Completing the Square

5Complex Arithmetic

Adding and Subtracting Multiplying The Conjugate Dividing A Pure Imaginary Bottom Recap: Complex Arithmetic

8Lines Meet Parabolas

Two Crossings Just Touching No Meeting A Circle and a Line Recap: Lines and Parabolas

3Vertex Form by Algebra

From Standard to Vertex Odd Middle Terms A Leading Number Opening Down Recap: Vertex Form

6Complex Solutions

Squares Equal to Negatives A Shifted Square The Formula Goes Complex Fractions in the Answer Recap: Complex Solutions

9Quadratic Models

The Highest Point Back to the Ground The Biggest Area Price and Revenue Recap: Models