Quadratic Graphs - Part 2

CREDITS
Animation & Design: Jean-Pierre Louw
Narration: Lucy Billings
Script: Lucy Billings

In this video we are going to discover even more information connecting the quadratic equation with it’s graphed function. We will look at the turning points - so the maximum and minimum. These are also known as the vertex. Quadratic functions are symmetrical. They have a line of symmetry which is known as the axis of symmetry.

The turning point will always sit on the axis of symmetry. In a positive quadratic, the turning point is a minimum… it is the lowest point of the function. And in a negative quadratic the turning point is a maximum… it is the highest point of the function.

We can easily find the x-coordinate of the turning
point by using this simple little equation…
x = 2a
−b
axis of symmetry, x = 2a where
−b y = ax2 + bx + c

So b is the value in front of the x in the equation
And a is the value in front of the x2
So let’s check it for this graph…

A is 1
And b is -2

So the axis of symmetry = - -2 / 2 X 1
So 2 / 2 which is 1.
So x = 1

we can find out the y-coordinate of the turning point. Not just the line of symmetry. We use our x value from the axis of symmetry… and just substitute that into the original quadratic equation. So the coordinates of the turning point are (1, -4)

So that’s the final piece of the puzzle when sketching quadratics… now let’s combine our knowledge of the roots, and the y-intercept with the turning point so
that we can sketch a quadratic showing it’s correct shape and labelling 4 points on the function.

So that’s the axis of symmetry which we use to find the coordinates of the turning point. You are usually given the little formula, but check on your formula sheet or with your teacher as you may need to memorise. And then you substitute the x value into the quadratic to find the y-coordinate.