### 7.2 Properties of the Quadratic Formula

Some curricula feel it is important to notice that the formula

$$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$$

represents two symmetrical values about the middle point $$x=-\frac{b}{2a}$$.

From part 4 of this course we know that the vertex of the parabola lies halfway between any two symmetric points. Our technique of simply looking for interesting $$x$$-values makes the location of the vertex clear. One need not know this formula.

(But if you do want it … just write $$y=ax^{2}+bx+c$$ as $$y=x(ax+b)+c$$. This shows that inputs $$x=0$$ and $$x=-\frac{b}{a}$$ give symmetrical outputs. The vertex is thus halfway between these values … at $$x=-\frac{b}{2a}$$!)

## Books

Take your understanding to the next level with easy to understand books by James Tanton.

BROWSE BOOKS

## Guides & Solutions

Dive deeper into key topics through detailed, easy to follow guides and solution sets.

BROWSE GUIDES

## Donations

Consider supporting G'Day Math! with a donation, of any amount.

Your support is so much appreciated and enables the continued creation of great course content. Thanks!