A curve has equation \(y=x^{2}+2 x-3\). (a) Use the method of completing the square to find the coordinates of the stationary point on the curve.

(b) On the axes, sketch the curve, stating the intercepts with the coordinate axes.

(a) Write \(3+4 x-2 x^{2}\) in the form \(a+b(x+c)^{2}\), where \(a, b\) and \(c\) are integers. (b) Hence write down the range of the function \(\mathrm{f}(x)=3+4 x-2 x^{2}\), where \(x \in \mathbb{R}\).

(a) Write \(19-12x-3x^2\) in the form \(a(x+b)^2+c\), where \(a\), \(b\) and \(c\) are integers.

(b) Hence find the maximum value of \(19-12x-3x^2\) and the value of \(x\) at which this maximum occurs.

(c) Use your answer to part (a) to solve the equation \(19-12\sqrt u-3u=0\).

(a) Write \(2x^2+5x+3\) in the form \(2(x+a)^2+b\), where \(a\) and \(b\) are rational numbers.

(b) Hence write down the coordinates of the stationary point on the curve \(y=2x^2+5x+3\).

(c) Solve the inequality \(2x^2+5x+3\lt\frac{15}{8}\).

(a) Write

\(3x^2+15x-20\)

in the form \(a(x+b)^2+c\), where \(a\), \(b\) and \(c\) are rational numbers.

(b) State the minimum value of \(3x^2+15x-20\) and the value of \(x\) at which it occurs.

(c) Use your answer to part (a) to solve the equation

\(3y^{2/3}+15y^{1/3}-20=0,\)

giving your answers correct to three significant figures.

(a) Write the expression

\(x^2-6x+1\)

in the form \((x+a)^2+b\), where \(a\) and \(b\) are constants.

(b) Hence write down the coordinates of the minimum point on the curve

\(y=x^2-6x+1.\)

(a) Write \(9x^2-12x+5\) in the form \(p(x-q)^2+r\), where \(p\), \(q\) and \(r\) are constants.

(b) Hence state the coordinates of the minimum point on the curve \(y=9x^2-12x+5\).

(i) Express \(5x^2-15x+1\) in the form \(p(x+q)^2+r\), where \(p\), \(q\), and \(r\) are constants.

(ii) Hence state the least value of \(x^2-3x+0.2\) and the value of \(x\) at which it occurs.

(i) Given that \(y=2x^2-4x-7\), write \(y\) in the form \(a(x-b)^2+c\), where \(a\), \(b\) and \(c\) are constants.

(ii) Hence write down the minimum value of \(y\) and the value of \(x\) at which it occurs.

(iii) Using your answer to part (i), solve

\(2p-4\sqrt p-7=0,\)

giving your answer correct to 2 decimal places.

(i) Write

\(8+7x-x^2\)

in the form \(a-(x-b)^2\), where \(a\) and \(b\) are constants.

(ii) Hence state the maximum value of \(8+7x-x^2\) and the value of \(x\) at which it occurs.

(iii) Using your answer to part (i), or otherwise, solve the equation

\(8+7z^2-z^4=0.\)