Coaching Centre
Non-linear graphs
Recognising and plotting simple non-linear relationships such as parabolas y = x² + c, and telling linear from non-linear rules and tables.
Parabolas
The graph of $y = x^2$ is a U-shaped curve called a parabola. Its lowest point, the turning point or vertex, is at $(0, 0)$.
Adding c moves the parabola up or down without changing its shape.
Is this table linear? $x = 0, 1, 2, 3$; $y = 1, 2, 5, 10$.
Is $x = 0, 1, 2, 3$; $y = 1, 2, 5, 10$ linear?
Differences $1, 3, 5$ are not constant.
Find the $x$-intercepts of $y = x^2 - 4$.
$x^2 = 4$.
Find the turning point of $y = x^2 + 1$. Enter $x, y$.
The parabola $y = x^2$ moved up $1$.
Which rule is linear?
Only power of $x$ is $1$.
For $y = x^2 + 4$, find $y$ when $x = -3$.
$9 + 4$.
How many $x$-intercepts does $y = x^2 + 2$ have?
Its lowest point is $(0, 2)$, above the axis.
Is $x = 0, 1, 2$; $y = 7, 4, 1$ linear?
Differences are all $-3$.
Find the $y$-intercept of $y = x^2 - 5$.
Set $x = 0$.
New numbers every time. Keep going until you get five in a row.