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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).
$ h(x) = x^2 - 8x + 16 $
Vertex: $(4,0)$Axis of symmetry: $x=4$$x$ -intercepts: $(4,0)$
Polynomial and Rational Functions
Quadratic Functions and Models
Harvey Mudd College
Idaho State University
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Let's grab the following function. H now notice that we can rewrite. This is the following. You could go ahead and verify this if you use foil method to distribute this polynomial. And the nice thing about this is that this is the standard form. But really the way to get to this graphic stitches Start off with the basic Graff X squared. We know how to graft this proble so I'll do this one in red So here's a rough sketch of the X Square Graff proble And then now the next step is to subtract X Excuse me, subtract four from the ex and with that, those is that shift four units to the rain. So that means we just take each point on the red graph and movement over four to the right, so that will be the vertex. And then go ahead and move those other points over a cz well, and so there's a rough sketch of the problem. This is a church, and the next we want to label the Vertex. You could even read this from the standard form. Or you can just see the point over here is for comma zero. The access of cemetery. That's always a vertical line passing through the Vertex. So there's a rough sketch of that should be a straight line there, and we see that this is X equals four. This is the Axis and the ex intercepts. You can see that so you would set H people to zero. And you see that the solution to this it's X minus four equals zero, So X equals four, so we only have one intercept x intercept, and the point is for comma zero.
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