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Advanced 𝑥 Algebra Topic 49 of 100

Parabolas and Vertex Form

Graph of a quadratic; vertex at (h,k).

Key idea

Graph of a quadratic; vertex at (h,k).

In depth

y = a(x − h)² + k places the vertex at (h, k). The sign of a decides whether it opens up or down, and its size controls the width. Vertex form shows transformations directly.

Worked example

y = 2(x − 3)² + 1 has vertex (3, 1), opens up, narrower than y = x².

Formula

y = a(x−h)² + k

Real-world uses

Common mistake

Reading h with the wrong sign: (x − 3) means h = 3, not −3.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Parabolas and Vertex Form?

Graph of a quadratic; vertex at (h,k). It is a topic at the advanced level in Algebra.

What is the formula for Parabolas and Vertex Form?

The key formula is y = a(x−h)² + k.

Where is Parabolas and Vertex Form used in real life?

Real-world examples: Designing satellite dishes, bridge arches and headlight reflectors; Finding the highest point of a path.

What should I learn before Parabolas and Vertex Form?

Make sure you are comfortable with Discriminant, the previous topic in Algebra.

What is a common mistake with Parabolas and Vertex Form?

Reading h with the wrong sign: (x − 3) means h = 3, not −3.

How can I practise Parabolas and Vertex Form?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Parabolas and Vertex Form?

Move on to Quadratic Axis of Symmetry next.

Related advanced topics in Algebra