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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 + 4)^2 - 3 $

Vertex: $\quad(-4,-3)$Axis of symmetry: $x=-4$$x$ -intercepts: $(-4 \pm \sqrt{3}, 0)$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

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we can use transformations of the proble X squared to graph our function. So first licious go give a rough sketch of ex Claire. So this is not our actual answer. This is just a thirty point here. Okay, So first step is to just add for tow X And so this is a shift to the left by four units. So that means you take each point on the black dotted breath and go to the left by four. So the vertex goes on the left over here in minus four and so on. And then finally, to get our function of you, take the previous graph and red, and then you shift that down by three units. So that means we take each red point and bring it down by three. So the vertex now becomes the point minus four minus three. And you could even go ahead and plot another point or two. So this point right here, minus three minus two. And this point over here, minus five, minus two. So, using transformations, we've given the graph of F. So that's in greed. Identify the birth texts. We already did. That access is symmetry. The access the cemetery is the vertical line that passes through the verse six. So any point on this line, we have X equals four. So that's the equation for the line. Let me just abbreviate this access of symmetry and the ex intercepts will those we could just go ahead and find. So go ahead and set this quantity equal to zero. So you can see that both of these numbers are negative. And we have minus four minus through three comma zero minus four plus through three comma zero. The's are the ex intersex and graphically thes points are located here and over here.

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