Problem

In Exercises 17-34, sketch the graph of the quadr…

02:46

Problem 24 Easy Difficulty

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 - 6)^2 + 8 $

Answer

Vertex: $(6,8)$
Axis of symmetry: $x=6$
$x$ -intercepts: None

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Algebra

Precalculus with Limits

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

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Video Transcript

Let's graft this quadratic function f without using a graphing utility. And then we'LL give some information. That's the Vertex access, the symmetry and ex intercepts. So here is usual. I would just start off with ex clear and then build my way up Teo f by doing transformations one at a time. So start off with usual X squared. We know what the graph looks like. So we could even give a rough sketch over here of X squared. So this is not our final answer. This is X squared right here and read. The first step would be to subtract six from the eggs and this case, this's a shift. Six units to the right. So each point on the red graph gets food over to the right by six. So the birth hex of the ex square gets moved over here and vice versa, and so on for all the other points. And once again, this green is not our final draft because we have one more transformation to apply. So, Abel, this graph X minus six squared and then finally we get tough if we just add eight to this previous expression. So we're not adding it to the X for adding it to the whole expression. So that means that this is the shift eight units up. So each point on the green Graff gets moved up eight units, so the Vertex for the green was six zero. Now that gets moved up to the point six eight. We'LL label that because that's one of the answers here and let's plot a few more points. So take those other points on your graph and move them all up by a units. And here's a rough sketch of our final graph F. And so now let's go read the information. The Vertex We label that that's the point sixty eight access of symmetry. That's always the world call line, passing through the problem, cutting it in half. So each point on this line has in common that the exile US six. So that's the access of symmetry and excel ourselves. Just I'm looking at the graph. We see that there are no ex intercepts. No, another way to see this is is by setting this equal to zero you'LL see that it has no solution. If this equal zero then you could subtract, eh? But this could never happen because this expression on the left is always bigger than or equal to zero because it's a square square cannot be negative, so this has no solution. Therefore, as our graph suggest, there are no eggs intercepts.

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