01 – Find roots, turning points graphically
If you plot a quadratic equation you get a quadratic graph.
The Roots are the solutions to the equation.
You can solve quadratics equations graphically or by an algebraic method like completing the square.
Completing the square also provides information on how to sketch a quadratic equation.
Look at the quadratic graph (plotted from a quadratic equation).
A turning point is where the gradient is zero.
To find the ROOTS of an equation you need to solve the equation to find the values of x.
If you have a graph, you can do this by finding where the graph cuts the x-axis.
If you have to deduce the roots of a quadratic equation algebraically, use methods like factorising or completing the square to solve the quadratic equation.
Write down the co-ordinates of the turning point.