This week in math 11 we learned how to determine whether or not a parabola opens up or down(positive or negative), if it is congruent, and how to find the vertex. This can all be done just by looking at the function.
For example, if the function looks like 
you know this function opens up because the 
is positive (keep in mind there is an imaginary 1 out front as well). If you were given the equation 
you would know this one opens down because the 2 is negative, you also know the vertex. The vertex for this would be (4,-7),the reason that the 4 is positive and not negative is because you are creating a zero pair for the number inside the bracket (always using the opposite sign), the -7 states the same and this goes for finding any vertex. This parabola is also not congruent, this is because of the 2 out front. since there is a number greater than 1 out front this means that the parabola is a stretch meaning it won’t be able to follow the 1,3,5 rule that would make it congruent (up one over one, up three over one, up 5 over one). This would go the same for a fraction as well. If the function was then since there is the imaginary 1 out front this makes the function congruent.
By being able to look at the function and determine these things it will save you time since you won’t have to make a table of values, of coarse the table is always a good back up to use if you get stuck.
