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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).

$ g(x) = x^2 + 2x + 1 $

Vertex: $(-1,0)$Axis of symmetry: $x=-1$$x$ -intercepts: $(-1,0)$

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 graft this quadratic function. G There are many ways to graph this one ways to use transformations of your usual proble X squared. So to do that here I'LL just take this G function and you could complete the square. Actually, this is already a square you can just write. This is explicit and square. And so we know autograph X squared the way to go from X square toe X plus one square is a shift to the left one unit eat. So in this case, we would just take our usual proble X squared and push every point over one unit to the left. So instead of having a point of zero, zero, will be a negative one zero and so on. So here are a few points and then we could just give a rough looking sketch here of our of our graph. And if you want a more realistic looking graph, you could always plug in a few more points. But here's a rough sketch of our problem, Jean. So that's the first part of this question was to sketch the graft and then the next part is tto find some more information, so identify the birthday cakes. In this case, we can just look at the graph and we see that the text of the X Square just moved over one to the left. But in general, the formula would be Excuse me here. So and actually another way to see that this is the Vertex is that if you look at the standard form, this has Vertex h calm, okay? And in our case, you can see that we're not adding anything, So it's the k A zero. And that you can rewrite. This is X minus negative, one square. So in our case, you can see that each is negative one in that case, zero. So that answers that question. That's our politics. Assets of symmetry. This is always X equals age. So in our case, that just becomes X equals negative one. And you could see that over here on the graph. It's a rough sketch of the axis of symmetry. X equals minus one vertical line, and then X intercepts is well, in this case, we could see that we have only one intercept and it's at the Vertex and the graph, the vertex, the intercepted, the accesses imagery. This gives us our final answer

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