10E

Sketching parabolas

Sketching parabolas from intercept form y = (x − a)(x − b) and from y = x² + bx + c by finding intercepts, the axis of symmetry and the turning point.

From intercept form

Example 1●●

Sketch $y = (x - 1)(x + 3)$.

$x$-intercepts $1$ and $-3$. Axis $x = -1$.

Turning point: $y = (-2)(2) = -4$, so $(-1, -4)$.

$y$-intercept: $(-1)(3) = -3$. Concave up.

Intercept form

The turning point is always directly between the two x-intercepts.

Flashcards

$x$-intercepts of $y = (x - 2)(x + 6)$

$2$ and $-6$

Axis from intercepts

Average of the intercepts

Four things to label

Both $x$-intercepts, $y$-intercept, turning point

Practice

Turning point of $y = (x - 1)(x + 3)$?
$y$-intercept of $y = (x - 1)(x + 3)$?
$x$-intercepts of $y = (x - 2)(x + 6)$?
Axis of symmetry of $y = (x - 2)(x + 6)$: $x = $ ?
Minimum value of $y = (x - 2)(x + 6)$?
Turning point of $y = x^2 - 6x + 8$?
$x$-intercepts of $y = x^2 - 4x$?
$y = -(x - 1)(x - 5)$ is: