Revision sheet

Quadratic patterns

Constant second differences mean quadratic.

Watch out: growing differences are not linear.

Polynomial arithmetic

• Add: combine like terms.
• Multiply: every term by every term; degrees add.

Watch out: $x$-terms add; constants multiply.

Standard and factored form

Factored form gives the $x$-intercepts; standard form gives the $y$-intercept.

Watch out: the factor $x + 5$ gives the intercept $-5$.

Graphs of quadratics

Sign of $a$: up or down; $c$: $y$-intercept; vertex midway between the zeros.

Watch out: the $y$-intercept is $c$, not $a$.

Quadratic functions

1. Vertex at $x = -\dfrac{b}{2a}$.
2. Its height $f\left(-\dfrac{b}{2a}\right)$ is the minimum ($a > 0$) or maximum ($a < 0$).
3. Vertex form: $a(x - h)^2 + k$, vertex $(h, k)$.

Watch out: the constant term $c$ is $f(0)$, not the extreme value.

Vertex form

$y = a(x - h)^2 + k$: vertex $(h, k)$.

Watch out: $(x + h)$ means the vertex is at $-h$.