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In Exercises 17-34, sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s).

$ f(x) = - x^2 - 4x + 1 $

Vertex $(-2,5)$symmetry axis $x=-2$$x$ -intercepts $(-2-\sqrt{5}, 0),(-2+\sqrt{5}, 0)$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Campbell University

Idaho State University

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first write F in the Vertex form. So this will be something like and then our vertex will be the point. I'm scared. Okay, So let me go ahead and pull out a negative sign just from the first two terms. Now go ahead and take half of four and square that and you get four back. But notice we didn't just ad for and really, we didn't mind us for here, So make up for that by adding forthe variant. Go ahead and complete that square. And there we are. Theirs are for takes form so many ways to could go ahead and get the rest of the graph. You go. You can go ahead and just plugging a few more points here. Or you can just see that this is a transformation of X squared. But if you want to go ahead and just plugging a few points here, you could plug in negative one. You get four. He plugged in negative three. You also good for and then half of zero. That should give you one. And if you do f of minus four, that should also give you one. So there's a few points and let's go ahead and give a rough sketch here and less Label of Vertex. Negative to five. Okay, so photograph a rough sketch. Okay, so then completes this part. Sketched the graph now identified. The verse six where we have that access of cemetery. This has always given my X equals h. In our case, H is minus two. So we'LL say X equals minus two. This is the axis and finally, the ex intercepts. So we're trying to find out what these two points are. So we'LL go ahead and set f equal to zero. So that becomes Take the square ruler on both sides. Don't forget the plus and minus and then subtract it too. So these will be our X intercepts.

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