Question 22916
Ok, you can show x squared like this...x^2 by using the caret (^).  You get the caret by Shift-6 key. A little advice...use the same type letter (all upper case or all lower case) for the variable in your problems, rather than swithichjng from X to x and back again.

Solve: You can also write your equation: {{{y = x^2 + 6x + 5}}}
{{{y = x^2 + 6x + 5}}} You can solve this by factoring if you set y = 0
{{{(x + 1)(x + 5) = 0}}} Apply the zero product principle.
{{{(x + 1) = 0}}} and/or {{{(x + 5) = 0}}}
If {{{x + 1 = 0}}} then, {{{x = -1}}}
If {{{x + 5 = 0}}} then, {{{x = -5}}}

The x-intercepts (also called zeros) are:
{{{x = -1}}}
{{{x = -5}}}

The x-coordinate of the vertex is found by:
{{{x = -b/2a}}} The a and b come from the standard form of the quadratic equation: {{{ax^2 + bx + c}}} In your equation, a = 1 and b = 6

{{{x = -6/2}}}
{{{x = -3}}} This the x-coordinate of the vertex.  Find the y-coordinate by substituting this value of x into your equation and solving for y.

{{{y = x^2 + 6x + 5}}} x = -3
{{{y = (-3)^2 + 6(-3) + 5}}}
{{{y = 9 - 18 + 5}}}
{{{y = -4}}}

The vertex is at (-3, -4)

Here's the graph.
{{{graph(300,200,-10,3,-5,5,x^2+6x+5)}}}