9.2 Vertex Form and Transformations

3 practice questionsNot yet reviewed

Notes

Vertex form $f(x) = a(x - h)^2 + k$ shows the vertex $(h, k)$ right away.

Compared with $y = x^2$: $h$ shifts right ($h > 0$) or left; $k$ shifts up or down.
$|a| > 1$ stretches it (narrower); $0 < |a| < 1$ compresses it (wider); $a < 0$ flips it upside down.
Watch the sign: $y = (x + 3)^2$ has $h = -3$, a shift left.

What is the vertex of $y = 2(x - 5)^2 + 1$?

Compared with $y = x^2$, the graph of $y = (x + 4)^2 - 2$ is shifted:

Which parabola is narrowest?