Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

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Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Find $p$ and $q$ such that $ax^2+bx+c = a(x+p)^2+q$. 

Hence, or otherwise, find roots of  $ax^2+bx+c=0$.

Includes a video which shows how to solve a quadratic by completing the square.

Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Find $B$ and $C$ such that $x^2+bx+c = (x+B)^2+C$.

Find $a$, $B$ and $C$ such that $ax^2+bx+c = a(x+B)^2+C$.

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$.  Find both roots of the equation $q(x)=0$.

Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.

Completing the square twice to determine the radius and centre of a circle.

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Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Find $c$ and $d$ such that $x^2+ax+b = (x+c)^2+d$.