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To find the x intercepts, we need to put the standard form equation into factored form.
Which two numbers multiply to -8 and add to -2?
So the factored form is
That means the x intercepts are at
So now we have the x intercepts.
To find the vertex, we need to convert the standard form equation into vertex form.
The formula of vertex form is
Since the a value in the standard form equation is 1, the a value in vertex form is also one.
The h value can be found using the formula
Which comes out to or 1.
To find the k value, we can just plug in what we got for h back into the equation.
So the vertex is .
This also means the axis of symmetry is
Finally, to find the y intercept, we plug in 0 for x and solve.
So the y intercept is .
It's a factor. This concept is widely used throughout algebra, and you'll probably bump into it through the end of high school and beyond.
A common use is expressing a term in <em>prime factorization</em>, or reducing a number to its most base parts- primes. For example:
Of course, a number like 13 which is already prime is made up of itself and 1. <em>Factors do not have to be primes.</em> 20 is also reducible through combinations of 1, 2, 4, 5, 10, and 20. Prime factorization is just a handy example.
Basically, factors multiply with each other to create other numbers, and numbers can be reduced down to their factors.