The tutor shows how to convert a quadratic function from standard form to vertex form.

Quadratic functions are often written in standard form

y=ax²+bx+c

but more useful is vertex form

y=a(x-p)²+q

A quadratic function in standard form can be converted to vertex form. One method is completing the square; see my post here for an introduction.

Example.

Convert y=x² -10x -1 to vertex form.

Step 1: Rewrite the equation, leaving a space before the constant:

y=x² -10x     -1

Step 2: Take half the coefficient of the x term and square it.

Here, the coefficient of the x term is -10. Half is -5; (-5)²=25.

Step 3: Both add and subtract the squared value to the right side of the equation:

y=x² -10x  +25 -1 -25

Step 4: Notice that the first three terms on the right side form a perfect square trinomial:

y=(x² -10x +25) -1 -25  becomes y=(x-5)²   -26

[Reason: (x-5)²=(x-5)(x-5) = x² -5x -5x +25 = x² -10x +25, by foil method]

Step 5: Apparently, vertex form of y=x² -10x -1 is y=(x-5)² -26. The vertex is (5,-26). (To identify the vertex, see my post here.)

Next post, I’ll be covering the case where the coefficient of x² is other than 1. It will be dependent on the technique described here.

HTH:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.