# How do you find the vertex of y=x^2+9x+8?

Feb 24, 2016

color(blue)("A neat trick to find "x_("vertex"))

#### Explanation:

Consider the standard for$\text{ } y = a {x}^{2} + b x + c$.........(1)

rewritten as:$\text{ "y=a(x^2+color(red)(b/ax))+c" } \ldots \ldots \ldots \ldots . \left({1}_{a}\right)$

Now compare it to your question's format

$\text{ } y = {x}^{2} + \textcolor{g r e e n}{9 x} + 8$.......................(2)

In equation (2) $\textcolor{red}{a = 1}$ so for this equation we have

 color(red)(b/a x) -> color(green)((9x)/color(red)(1) = 9x
'~~~~~~~~~~~~~~~~~~~~~~~~~
Hears the sneaky bit!

x_("vertex")" "=" "(-1/2)xxa/b" " ->" " (-1/2)xx9 " "=""- 4 1/2

So by substituting $x = - 4 \frac{1}{2}$ into equation (2) you can determine the value of $y$