Mathematics·Functions and graphs · NSSCO 7.3
Quadratic & other graphs
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The quadratic gives us the beautiful curve called the parabola, and this lesson shows you how to draw it and read all its secrets. We build a table of values, plot the points and join them into a smooth curve, then read off the line of symmetry, the turning point (minimum or maximum) and the roots. We use the graph to solve equations, learn the completing-the-square shortcut to the turning point, and finish by recognising three more graph shapes you must know — the cubic, the reciprocal and the exponential.
What you'll learn in this lesson
By the end you should be able to (NSSCO Mathematics 7.3):
- Construct a table of values for a quadratic function y = ax² + bx + c
- Plot the points and draw a smooth parabola from the table
- Identify the parabola's shape and its line of symmetry (including x = −b/2a)
- Read the turning point (minimum or maximum) and the roots (x-intercepts) from the graph
- Use a graph to solve quadratic equations approximately, including by drawing a line
- Find the turning point by completing the square, and sketch a quadratic from its key points
- Recognise and sketch the cubic y = x³, the reciprocal y = a/x and the simple exponential y = aˣ
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