Year 10: Quadratic turning point

What is a Quadratic Turning Point?

A quadratic equation in the form y = ax² + bx + c has a ‘turning point’ – also known as a vertex – on its parabola. This turning point represents the minimum or maximum value of the quadratic function.

Finding the Turning Point

1. Standard Form: y = ax² + bx + c
2. x-coordinate of the turning point: x = -b / 2a
3. Substitute 'x' back into the equation to find the y-coordinate. y = a(-b / 2a)² + b(-b / 2a) + c = c

Using the Vertex Form

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) are the coordinates of the turning point.

In this form, the turning point is always at the point (h, k).

Example

Let's say y = 2x² - 8x + 6.

1. a = 2, b = -8, c = 6
2. x = -b / 2a = -(-8) / (2 * 2) = 8 / 4 = 2
3. y = 2(2)² - 8(2) + 6 = 8 - 16 + 6 = -2
4. The turning point is at (2, -2)

Remember to always consider whether the 'a' value is positive or negative, as this determines whether the parabola opens upwards (minimum) or downwards (maximum).