4 The variables \(x\) and \(y\) are related by an equation of the form
$$y = a x ^ { 2 } + b$$
where \(a\) and \(b\) are constants.
The following approximate values of \(x\) and \(y\) have been found.
| \(\boldsymbol { x }\) | 2 | 4 | 6 | 8 |
| \(\boldsymbol { y }\) | 6.0 | 10.5 | 18.0 | 28.2 |
- Complete the table below, showing values of \(X\), where \(X = x ^ { 2 }\).
- On the diagram below, draw a linear graph relating \(X\) and \(y\).
- Use your graph to find estimates, to two significant figures, for:
- the value of \(x\) when \(y = 15\);
- the values of \(a\) and \(b\).
| \(\boldsymbol { x }\) | 2 | 4 | 6 | 8 |
| \(\boldsymbol { X }\) | | | | |
| \(\boldsymbol { y }\) | 6.0 | 10.5 | 18.0 | 28.2 |
\includegraphics[max width=\textwidth, alt={}, center]{763d89e4-861a-4754-a93c-d0902987673f-05_771_1586_1772_274}