Question 278431
{{{g(x)=3x^2+2}}}
When working with functions it helps to look at a formula like this as a pattern. What this equation tells us is: "The function g takes its input, which we'll call "x" and it will square it, then multiply that by 3 and then add 3 to that." The function g, as defined above, will square, multiply by 3 and add 2 to <b>any</b> input you give it!<br>
g(x+a) means the input is x+a. And what will g do to its input? It will square it, multiply by 3 and add 2!
{{{g(x+a) = 3(x+a)^2 + 2}}}
which simplifies as follows:
{{{g(x+a) = 3(x^2+2ax +a^2) + 2}}}
{{{g(x+a) = 3x^2+6ax +3a^2 + 2}}}<br>
For g(x+a) - g(x) we substitute the expressions above:
{{{g(x+a) - g(x) = (3x^2+6ax +3a^2 + 2) - (3x^2+2) = 6ax + 3a^2}}}