Coaching Centre
The parabola
Features of a parabola: concavity, turning point, axis of symmetry and intercepts, and reading them from a graph or equation.
Features
Change a, b and c. The axis of symmetry is always halfway between the x-intercepts.
For $y = x^2 - 4x + 3$, find the intercepts, axis and turning point.
Turning point of $y = x^2 - 4x + 3$? Enter $x, y$.
Axis $x = 2$, $y = -1$.
$x$-intercepts of $y = x^2 - 4x + 3$?
$(x - 1)(x - 3)$.
$y$-intercept of $y = x^2 - 4x + 3$?
Set $x = 0$.
Axis of symmetry of $y = x^2 + 6x + 1$: $x = $ ?
$-\tfrac{6}{2}$.
$y = -2x^2 + 5$ is:
$a = -2 < 0$.
Maximum value of $y = -2x^2 + 5$?
Turning point $(0, 5)$.
A parabola has $x$-intercepts $-3$ and $5$. Axis: $x = $ ?
Halfway: $\tfrac{-3 + 5}{2}$.
Minimum value of $y = x^2 - 4$?
Turning point $(0, -4)$.
New numbers every time. Keep going until you get five in a row.