Find the coordinates of the turning point of the curve $y=7+5x-x^2$, stating whether it is a maximum or a minimum point.

Express $2x^2+9x+4$ in the form $a(x+b{)}^2+c$, where $a, b$ and $c$ are constants.

Write down the coordinates of the vertex of the curve $y=2x^2+9x+4$, and state whether this is a maximum or a minimum point.

Find the minimum value of $x^2-7x+8$ and the corresponding value of $x$.

Write $1+x-2x^2$ in the form $p-2(x-q{)}^2$.

Sketch the graph of $y=1+x-2x^2$.

Prove that the graph of $y=4x^2+2x+5$ does not intersect the $x-$axis.

Find the equations of parabolas $A, B$ and $C$.

A parabola passes through the points $(0,-24),(-2,0)$ and $(4,0)$. Find the equation of the parabola.