A quadratic graph is produced when you have an equation of the form \(y = ax^2 + bx + c\), where \(b\) and \(c\) can be zero but \(a\) cannot be zero.
All quadratic graphs have a line of symmetry.
Positive quadratic graphs (where \(a \textgreater 0\)) are U-shaped and have a turning point at the bottom of the curve. Negative quadratic graphs (where \( a \textless\)) are ∩-shaped and have a turning point at the top of the curve.
Draw the graph of \(y = x^2 – x – 4\)
First we need to complete a table of values:
\[x\] | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|---|---|---|
\[y\] | 8 | 2 | -2 | -4 | -4 | -2 | 2 | 8 | 16 |
Then plot these points and join them with a smooth curve.