WEEK 6 — Quadratics & Parabolas (Gentle Introduction)

 


Welcome to Week 6 of your eight-week maths catch-up plan.
This week introduces quadratic functions and the curved shapes called parabolas.
We keep everything simple, visual, and stress-free — no heavy algebra, just clear understanding.

The video at the top of the page gives you the full lesson.
Below you’ll find the mind map, the day-by-day breakdown, practice exercises, and a short quiz.

Mind Map – Week 6


DAY 1 — What Is a Quadratic?

What to understand

A quadratic is a function with x² in it.
It makes a curved shape, not a straight line.

Examples:
• f(x) = x²
• f(x) = x² + 2
• f(x) = x² – 4

Practice

  1. Say if each is quadratic or not:
    – x² + 1
    – 2x
    – x² – x
    – 5x – 3

DAY 2 — Parabola Shape

What to understand

Quadratics make parabolas:

• If the x² term is positive → U-shape (opens up)
• If negative → upside-down U (opens down)

Examples:
• y = x² → opens up
• y = –x² → opens down

Practice

Say if each opens up or down:
2. y = 3x²
3. y = –2x²
4. y = x² – 4
5. y = –x² + 1

DAY 3 — Vertex (Turning Point)

What to understand

The vertex is:
• the lowest point (opens up)
• the highest point (opens down)

y = x² → vertex at 0
y = x² + 2 → moved up
y = x² – 3 → moved down

Practice

  1. For y = x² + 5 → is the vertex above or below the origin?

  2. For y = x² – 2 → above or below?

  3. For y = –x² + 4 → is the vertex highest or lowest?

  4. For y = –x² – 1 → highest or lowest?

DAY 4 — Table of Values (Creating a Curve)

What to understand

Choose x values → square them → plot points → curve appears.

Example with y = x²:
x: –2, –1, 0, 1, 2
y: 4, 1, 0, 1, 4

Practice

Make a small table for:
10. y = x²
11. y = x² – 2
12. y = x² + 3

(Use x = –2, –1, 0, 1, 2)

DAY 5 — Mixed Practice (Revision)

Practice

  1. Is y = –x² increasing or decreasing overall?

  2. Does y = x² open up or down?

  3. Where is the vertex for y = x² + 4 (above or below)?

  4. Fill a table for y = –x² using x = –2, –1, 0, 1, 2

Weekly Quiz — Week 6

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(Paste the embed code in HTML view once your quiz is ready.)

If you’re stuck, check the mind map or rewatch the video.

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