Non-Linear Graphs
Not all relationships are linear. Year 8 introduces parabolas (quadratic graphs), hyperbolas (inverse variation), and exponential curves, each with a distinctive shape and features.
What You Need to Know
Key Concept Diagram
A parabola (y = ax^2 + bx + c) is U-shaped, opening up if a > 0, down if a < 0
The vertex of a parabola is its lowest (or highest) point
A hyperbola (y = k/x) has two branches and asymptotes along the axes
An exponential curve (y = a^x) passes through (0, 1) and grows rapidly
Key Vocabulary
Parabola
The U-shaped curve produced by a quadratic equation y = ax^2 + bx + c
Vertex
The turning point of a parabola - the minimum or maximum point
Asymptote
A line that a curve approaches but never reaches
Hyperbola
The curve produced by an inverse variation y = k/x
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
For the parabola y = x^2 - 4, what is the y-intercept?
Question 2
Which graph has two branches that approach but never touch the axes?
Question 3
The graph of y = 2^x passes through which of these points?
Key Concepts Summary
- ●A parabola (y = ax^2 + bx + c) is U-shaped, opening up if a > 0, down if a < 0
- ●The vertex of a parabola is its lowest (or highest) point
- ●A hyperbola (y = k/x) has two branches and asymptotes along the axes
- ●An exponential curve (y = a^x) passes through (0, 1) and grows rapidly