Sketching Graphs Maths Methods Unit 1

When we talk about sketching a graph, we mean drawing a diagram showing the main features — not a true scale graph showing every point plotted accurately using a computer package or other means. To sketch a quadratic graph, the following features should generally be apparent or labelled: The y-intercept Any x-intercepts if they exist The turning point coordinates

Turning Point Form

Example 1 - the turning point form

Example 1

Example 1

Example 2 – the turning point form

Example 2 – the turning point form

Polynomial Form y = ax2 + bx + c Intercept Method

Polynomial Form y = ax2 + bx + c Intercept Method The coordinates of the turning point are

Polynomial Form y = ax2 + bx + c Intercept Method The y-coordinate of the turning point may be found by substituting the x-coordinate into the original equation.

Example 3 – Intercept Method Sketch the graph y = x2 + 10x + 25

Example 3

Example 4 Sketch the graph y = x2 − 16

Example 4

Example 5 Sketch the graph y = −2x2 + 11x − 15

Example 5 Sketch the graph y = −2x2 + 11x − 15