If the gradient of \(\left( {8,a} \right)\) and \(\left( {-1,3} \right)\) is \(2 \), find the value of \(a \).

Find the gradient of the straight line making an angle of \(60^\circ \) with the \(x\)-axis in the positive direction.

State the domain and range of \(y = \sqrt {1 – x} + 2\).

Given \(f\left( x \right) = 2x – 1\), \(g\left( x \right) = x + 1\), \(\left( {f \circ f} \right)\left( 2 \right) = a\), \(\left( {g \circ f} \right)\left( 1 \right) = b\), \(\left( {f \circ g} \right)\left( c \right) = 3\) and \(\left( {g \circ g} \right)\left( d \right) = 1\) find the domain and range of \(a + b + c + d\).

Find the expression of the parabola.

Find the coordinates of the vertex of $y=x^2-4x+5$.

Find \(c \), if the vertex of \(y = {x^2} – 6x + c\) is \(\left( {3, – 11} \right)\).

A quadratic graph cuts the $x$-axis at $2$ and $-\dfrac{1}{2}$, and passes through the point $(3,-14)$. Find $a,b$ and $c$, if the equation of the graph is $y=ax^2+bx+c$.

Find all values of \(k\) for which \(2{x^2} + \left( {k – 2} \right)x + 2 = 0\) has two real roots.

The solutions of \(3{x^2} – 6x = 2\) are \(A \pm \sqrt {\dfrac{B}{C}} \). Find \(A\), \(B\) and \(C\).