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In Exercises 57 and 58, determine the x-intercept(s) of the graph visually. Then find the x-intercept(s) algebraically to confirm your results.

$ y = x^2 - 4x - 5 $

$(5,0),(-1,0)$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

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Let's go ahead and graft this proble. And based on the graph, we'LL make a guest for the eggs intercepts and then we'll algebraic lee find X intercepts and computer results So photograph this one complied points Another method is just go ahead and complete the square So I see a four here on the X and negative for you Take half of that which is negative to square that you get four. So what I'LL do here is our ad in a four and then I'll make up for the adding the four by subtracting for a swell. So, as you can see, we really haven't changed the expression because these two will just cancel out Now The reason for doing this is that we could go on and simplify inside the prentiss he's and then we get the standard form. And the reason the standard form is useful is because if you know how to graft X squared, then you see our expression over here will be a shift to the right because we're subtracting too from the ex and then also here will shift down by nine and we could see that our vortex is the point too negative. Nine. So let's go ahead and plot that point in. There's two negative nine right down here. So there's a rough sketch and then we know that and the regular graph of X squared. If you go over one unit from the Vertex, then the Y value goes up. I want so we'LL use that fact here. Let's go over one unit. So here X equals one. Then we go up one unit to negative eight, and we can continue going in this fashion and so on. So from there and there's a rough sketch just based on three points, you can get a better looking Graff if you want to plug in a few more points here. So, looking at the rough guess that I gave here, I'm guessing that the intercepts. So this is the guest. Let's say X looks like about negative one half, and then maybe on this side, perhaps about X equals five. But we don't have to guess, because now we can algebraic Lee confirm. So let's do this in green. So here will use the quadratic formula. So we'LL have X equals negative B plus or minus, and then we have our square room B square minus four times a time. See and put that all over to a which is just too. So here I have four over to Celeste to and then plus or minus, and inside the radical will have sixteen plus twenty, so that will be two plus or minus. So radical thirty six is six. Divide that by two million three, and this is equal to either negative one or five. So these are our ex intercepts, and that's your final answer.

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