Year 10: Quadratic turning point

The turning point of a quadratic function (a parabola) is the maximum or minimum value the function attains. It's also known as the vertex.

Standard Form: $y=ax\mathrm{²}+bx+c$

In the standard form of a quadratic equation, $y=ax\mathrm{²}+bx+c$, the turning point has a specific x-coordinate:

Finding the x-coordinate of the turning point

The x-coordinate of the turning point is given by the formula:

  $x=-b/2a$

Where:
• 'a' is the coefficient of x²
• 'b' is the coefficient of x

Finding the y-coordinate of the turning point

Once you have the x-coordinate, substitute it back into the quadratic equation to find the corresponding y-coordinate (the turning point's coordinates).

Example:$y=2x\mathrm{²}-8x+6$

1. $a=2$, $b=-8$

2. $x=-(-8)/(2\times 2)=8/4=2$

3. Substitute $x=2$ into the equation: $y=2\left(2\right)\mathrm{²}-8\left(2\right)+6=8-16+6=-2$

Therefore, the turning point is at (2, -2).