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 = ax² + bx + c

In the standard form of a quadratic equation, y = ax² + 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 = 2x² - 8x + 6

1. a = 2, b = -8

2. x = -(-8) / (2 * 2) = 8 / 4 = 2

3. Substitute x = 2 into the equation: y = 2(2)² - 8(2) + 6 = 8 - 16 + 6 = -2

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