Chapter 13

Solve graphically the simultaneous equations $$ \begin{array}{r} 2 x-y=4 \\ x+y=5 \end{array} $$

Solve graphically the equations $$ \begin{gathered} 1.20 x+y=1.80 \\ x-5.0 y=8.50 \end{gathered} $$

Solve the quadratic equation. $$ 4 x^{2}+4 x-15=0 $$ graphically given that the solutions lie in the range \(x=-3\) to \(x=2\). Determine also the co-ordinates and nature of the turning point of the curve.

Solve graphically the quadratic equation \(-5 x^{2}+9 x+7.2=0\) given that the solutions lie between \(x=-1\) and \(x=3\). Determine also the co-ordinates of the turning point and state its nature.

Plot a graph of \(y=2 x^{2}\) and hence solve the equations: (a) \(2 x^{2}-8=0\) and (b) \(2 x^{2}-x-3=0\)

Determine graphically the values of \(x\) and \(y\). which simultaneously satisfy the equations $$ y=2 x^{2}-3 x-4 \text { and } y=2-4 x $$

Solve graphically the cubic equation $$ 4 x^{3}-8 x^{2}-15 x+9=0 $$ given that the roots lie between \(x=-2\) and \(x=3\). Determine also the co- ordinates of the turning points and distinguish between them.

Plot the graph of \(y=2 x^{3}-7 x^{2}+4 x+4\) for values of \(x\) between \(x=-1\) and \(x=3\). Hence determine the roots of the equation \(2 x^{3}-7 x^{2}+4 x+4=0\)