Graphs and Functions for GCSE

Introduction

Graphs and functions are integral to GCSE Maths, testing your ability to plot, interpret, and solve equations graphically. This article will cover:

1. Plotting and interpreting linear graphs.
2. Understanding quadratic and exponential graphs.
3. Solving equations graphically.

1. Plotting and Interpreting Linear Graphs

   Linear graphs have the equation , where:

   • : Gradient (slope).
   • : Y-intercept (where the graph crosses the y-axis).

   Example: Plot .

   1. Create a table of values:
      • For , .
      • For , .
      • For , .
   2. Plot the points: .

2. Understanding Quadratic Graphs

   Quadratics have the form .

   Key Features:

   1. Parabolic Shape: U-shaped or inverted.
   2. Vertex: Highest or lowest point.
   3. Axis of Symmetry: Vertical line through the vertex.

   Example: Plot .

   1. Create a table:
      • .
      • .
      • .
   2. Plot points and draw the parabola.

3. Solving Equations Graphically

   Graphs can help solve equations by finding where they intersect.

   Example: Solve .

   1. Plot .
   2. Find points where .
   3. Solutions: .

Practice Question

Question: Plot . Identify the gradient and y-intercept.

Solution:

• Gradient () = -1.
• Y-intercept () = 3.
• Plot the graph using points: .

Conclusion

Mastering graphs and functions equips you to solve equations visually and interpret real-world scenarios. Practise regularly to ace GCSE graph-related questions.