Factorising a quadratic expression of the form $x^2+bx+c$ by completing the square.

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Factorising a quadratic expression of the form $ax^2+bx+c$, where $a>1$.

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

Solving a quadratic equation of the form $ax^2+bx+c=0$ using the quadratic formula.

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Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

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.

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

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

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 $x^2+ax+b = (x+c)^2+d$.

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Entering the correct roots in any order is marked as correct. However, entering one correct and the other incorrect gives feedback stating that both are incorrect.

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

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

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

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$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(x-c)^{a/b}}$. Are there stationary points and local maxima, minima? Has $g$ a global max, global min?