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:
- Plotting and interpreting linear graphs.
- Understanding quadratic and exponential graphs.
- Solving equations graphically.
Plotting and Interpreting Linear Graphs
Linear graphs have the equation \( y = mx + c \), where:
- \( m \): Gradient (slope).
- \( c \): Y-intercept (where the graph crosses the y-axis).
Example: Plot \( y = 2x + 1 \).
- Create a table of values:
- For \( x = 0 \), \( y = 1 \).
- For \( x = 1 \), \( y = 3 \).
- For \( x = -1 \), \( y = -1 \).
- Plot the points: \( (0,1), (1,3), (-1,-1) \).
Understanding Quadratic Graphs
Quadratics have the form \( y = ax^2 + bx + c \).
Key Features:
- Parabolic Shape: U-shaped or inverted.
- Vertex: Highest or lowest point.
- Axis of Symmetry: Vertical line through the vertex.
Example: Plot \( y = x^2 – 4 \).
- Create a table:
- \( x = -2, y = 0 \).
- \( x = 0, y = -4 \).
- \( x = 2, y = 0 \).
- Plot points and draw the parabola.
Solving Equations Graphically
Graphs can help solve equations by finding where they intersect.
Example: Solve \( x^2 – 4 = 0 \).
- Plot \( y = x^2 – 4 \).
- Find points where \( y = 0 \).
- Solutions: \( x = -2, x = 2 \).
Practice Question
Question: Plot \( y = -x + 3 \). Identify the gradient and y-intercept.
Solution:
- Gradient (\( m \)) = -1.
- Y-intercept (\( c \)) = 3.
- Plot the graph using points: \( (0,3), (1,2), (-1,4) \).
Conclusion
Mastering graphs and functions equips you to solve equations visually and interpret real-world scenarios. Practise regularly to ace GCSE graph-related questions.
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