Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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So all we have to do is find the zeros of this equation. We can either use factoring or quadratic formula. What we have here though is our coefficient when x is negative which is sort of how to deal with, so what we can actually do is bring everything to the other side if we want to or factor out a -1.

I'm just going to factor out a -1, so what we end up with is -x² minus 4x plus 3. Now we just want to factor that down and we end up with x minus 3, x minus 1 giving us zeros of 1 and 3. So pretty easy way to deal with a negative sign is just to factor out.

So we found our x intercepts. The next thing we want to find is our y intercepts which we find by letting x equals 0. When we let x equals 0, our first two terms disappear and just leave us with -3, the last term.

To find the vertex, we can use -b over 2a. Our b is 4, so we end up with -4 over our a is -1, so we end up with -2 which gives us 2. That gives us the x coordinate of the vertex, so in order to find the y coordinate, we just have to go and plug 2 back in.

So we plugged 2 back in we end up with -4 plus 8 minus 3 which gives us 4 minus 3, 1. So using -b over 2a plug in to get the y coordinate, domain we're dealing with a parabola, our domain is always going to be all reals and our range, our range is our y values.

So for this one what we want to look at is our y coordinate the vertex which is 1. The negative on the x² tells us our parabola is facing downwards so we have a y coordinate of our vertex at -1 and our parabola goes downwards, sorry the y coordinate of the vertex at 1, parabola facing downwards, so we know that 1 is going to be the largest y value get. So our range then is just going to be from negative infinity up until 1 that point is on the curve so we include one with a hard bracket.

So finding a bunch of information about a quadratic intercepts just plug in 0 for the respective thing -b over 2a for your vertex domain and range.