Coaching Centre
Transformations of parabolas
Dilations y = ax², reflections y = −x², vertical and horizontal translations, turning point form y = a(x − h)² + k, and sketching from it.
Turning point form
a stretches or flips, h shifts left or right, k shifts up or down. The faint curve is y = x².
Find the turning point and $x$-intercepts of $y = (x + 1)^2 - 4$.
Turning point of $y = (x + 1)^2 - 4$?
$h = -1$, $k = -4$.
$x$-intercepts of $y = (x + 1)^2 - 4$?
$x + 1 = \pm 2$.
Turning point of $y = (x - 2)^2 + 3$?
Read $(h, k)$.
Compared with $y = x^2$, the graph of $y = 3x^2$ is:
$|a| > 1$.
$y = (x + 5)^2$ is $y = x^2$ shifted:
$x - h = x + 5$ gives $h = -5$.
$y = -(x - 1)^2 + 4$ has:
$a < 0$ and $k = 4$.
How many $x$-intercepts does $y = (x - 3)^2 + 2$ have?
Its minimum is $2$, above the axis.
$y$-intercept of $y = (x - 2)^2 + 1$?
$(0 - 2)^2 + 1$.
New numbers every time. Keep going until you get five in a row.