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Axis of Symmetry of a Parabola

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Axis of Symmetry of a Parabola

Study Guide

Key Definition

The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.

Important Notes

The axis of symmetry always passes through the vertex of the parabola.
The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.
For a quadratic function in standard form $y = ax^2 + bx + c$, the axis of symmetry is a vertical line $x = -\frac{b}{2a}$.
The axis of symmetry of a parabola opens upwards if $a > 0$ and downwards if $a < 0$.

Mathematical Notation

$y = ax^2 + bx + c$ represents a quadratic function.

$x = -\frac{b}{2a}$ is the formula to calculate the axis of symmetry.

Use variables and algebraic notation consistently; write equations clearly, and label the vertex when finding the axis of symmetry.

Why It Works

The axis of symmetry works because it represents a line of reflection. The parabola is symmetrical about this line.

Remember

Always substitute the values of a and b in the formula $x = -\frac{b}{2a}$ to find the axis of symmetry.

Quick Reference

Axis of Symmetry Formula:$x = -\frac{b}{2a}$

Understanding Axis of Symmetry of a Parabola

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the axis of symmetry of the parabola represented by the equation $y = 2x^2 + 3x + 1$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

John is throwing a ball in the air. The ball's height from the ground is represented by the equation $y = -x^2 + 10x + 0$. What is the time at which the ball will reach its highest point?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given the equation of a parabola $y = -2x^2 + 4x + 3$, determine whether the parabola opens upwards or downwards.

Challenge Quiz

Single Choice Quiz

Advanced

What is the axis of symmetry of the parabola represented by the equation $y = 3x^2 - 6x + 2$?

Recap

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