M4.9.6 For the adult
Graphs of quadratics
I plot the points of y = x² − 2x − 3 on a grid. What shape do they make?
What this chapter teaches
The graph of a quadratic is a smooth curve called a parabola. Its roots are where it crosses the x axis, its y axis crossing is the last number c, and its turning point is halfway between the roots. A table of values gives the points, which are joined by a smooth curve, never a ruler.
Three questions to ask
There is no one right wording. Listen for the idea.
- How do you work out y when x = −2 in y = x² − 2x − 3, and why is the answer positive?
- Where does the curve cross the y axis, and which number in the rule tells you?
- How can you find the turning point if you know the two roots?
After the chapter, the learner can
- Draw y = x² − 2x − 3 from a table of values
- Find the roots, turning point and y axis crossing from a graph
What they copy into their notebook
Make a table of values, plot the points, join them with a smooth curve. Roots: where y = 0. Crossing of the y axis: the last number. Turning point: halfway between the roots.