1.1 Quadratic Factorisation Worksheet

Express $2x^2-12x+7$ in the form $a(x+b{)}^2+c$, where $a$, $b$ and $c$ are constants.     [3]

Factorise correctly: $3x^2+13x-10$.

Factorise completely: $2x^2+16x+30$.

Factorise $49x^2-64$.

Factorise $20x^2-45$.

Solve the equation $2x^2-5x+1=0$, giving your answers in exact surd form.

Express $x^2+8x+3$ in the form $(x+a{)}^2+b$.

Express $2x^2-12x+7$ in the form $a(x+p{)}^2+q$.

A quadratic curve has the equation $y=-x^2+4x+5$.
1. Express the equation in form $a-(x+b{)}^2$.
2. State the coordinates of the turning point.

Find the coordinates of the intercepts with the axes for the curve $y=x^2-4x-12$.

Sketch the graph of $y=3+2x-x^2$. Show technical details including the $y$-intercept, $x$-intercepts, and the coordinates of the turning point.

A quadratic curve has its maximum turning point at $(2,9)$ and passed through the point $(0,5)$. Find the equation of the curve in the form $y=a{x}^2+bx+c$.

Solve the following equations:
a) $\frac{4}{x+1}+\frac{3}{x-1}=2$
b) $\frac{2}{x}+\frac{5}{x+3}=1$

Solve:
a) $\frac{3x^2+x-4}{x^2-4}=0$
b) $\frac{x^2-9}{5x+10}=0$

Solve:
a) $\frac{x^2-5x-6}{x^2+1}=0$
b) $\frac{2x^2+7x-4}{x^2+x+4}=0$

Find the real solutions:
a) $9(x^2-4x+3)=1$
b) $4(2x^2-x-5)=9$

Find the real solutions:
a) $(x^2-6x+5{)}^2=16$
b) $(2x^2-3x-2{)}^2=25$

A right-angled triangle has sides $(x+2)$ cm, $(2x+6)$ cm and 13 cm.
a) Show that $5x^2+28x-129=0$.
b) Find the lengths of the sides.

The area of a trapezium is 48 cm${}^2$. The parallel sides are $x$ cm and $(x+6)$ cm, and the height is $(x-2)$ cm. Find the value of $x$.

Solve $(x^2-7x+10{)}^{x^2-x-2}=1$.