2.1 Forms of Quadratic Functions

Notes

A quadratic function has degree 2. Its graph is a parabola. Each form shows something different.

• Standard form $y = ax^2 + bx + c$: the $y$-intercept is $c$, and the vertex is at $\displaystyle x = -\frac{b}{2a}$.
• Vertex form $y = a(x - h)^2 + k$: the vertex is $(h, k)$.
• Factored form $y = a(x - p)(x - q)$: the $x$-intercepts are $p$ and $q$.
• If $a > 0$ the parabola opens up; if $a < 0$ it opens down.
• Example: $y = x^2 - 6x + 5$ has vertex at $\displaystyle x = \frac{6}{2} = 3$, $y = 9 - 18 + 5 = -4$, so $(3, -4)$.