Problem

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

05:24

Problem 19 Medium 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^2 + 7 $

Answer

Vertex: $\quad(0,7)$
Axis of symmetry: $x=0$
x-intercepts: None

Related Courses

Algebra

Precalculus with Limits

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

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Video Transcript

for this problem Well liked to graph this function after this problem X squared plus seven and would identify the Vertex, the access of symmetry and the extent ourselves. So before we graph f and we'LL do that in red, let's just first take the graph of G X square and graft that problem. So if you plug in negative one or one into x square, you get one. If you plug in zero, you get zero. So we just get our usual. Our usual problem y equals X squared. There's a rough sketch of G but we are not interested in that graph. Our answer is the red graph. And the question is, how do we take this graph in black to obtain the graft that we want and red and we can see that that values of F or taking the X Square this is the same as the value of G and vicious adding seven. So this is a vertical shift by seven units. Okay, So that means that we'Ll just take any point on the original graph and just shipped it up by seven. So over here, when X is minus one, the Wye Valley was one, but then, for our graph will add seven to that martini. So there's eight up here, and so that will be our corresponding point. This y value at the first hex was originally zero at seven to that team seven that will give us our new Vertex. There it's Y equals seven and then, similarly, a one before why value was one. And then when we add seven to that, we obtained aid again. So there's on third point. And then let's just go ahead and give a rough looking sketch of another problem here. So same shape is the black craft. All we did was push it up by seven units. So this is our graph and red don't include the black one in the final answer. If you're using pencil, you want to go in their embrace. The G graph. Now we have some more questions. The answer and the first one is, is what is the Vertex. Originally, you see that the vortex was zero zero. You shift that out by seven. That pushes your vortex to the point zero seven. In general, for more complicated transformations, the verse hex has always given by the coordinates negative B over two a and then f negative b over to it. And our problem. We see that a is one and be a zero is the coefficients of X Square and the coefficient of X. The next one is the access of symmetry. If you look at the graph, you can see that it's the vertical line that passes through the Vertex. So in this case it will just be the Y axis. So there's a rough sketch of the access of symmetry, so this will be it's right this out access of symmetry. So this is given by General of formulas, negative B over two A. And in our case, that's just zero. So X equals zero. And finally, for the ex intercepts. Well, by looking at the graft, you could see that the smallest, why value seven. This graph will not pass the exam actions. And another way to see that is, if you took your F and you said it equal to zero. This has no solutions in the real numbers. So this no solution and that's why our answer is none for the ex intercepts. So that answers all the questions. That's our final answer

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