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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) = 16 - \frac{1}{4} x^2 $
Vertex: $\quad(0,16)$Axis of symmetry: $\quad x=0$$x$ -intercepts: $\quad( \pm 8,0)$
Algebra
Chapter 2
Polynomial and Rational Functions
Section 1
Quadratic Functions and Models
Quadratic Functions
Complex Numbers
Polynomials
Rational Functions
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is that we can grab f I just starting with the graph of X squared and doing a few steps here, and it's important to know which each step does photograph of the previous function. So here we take our original problem. Multiply by one over for so this is a vertical stretch by a factor of one over four. Here you see the negative sign. So we flipped the graph about the X axis and then finally the plus sixteen. This is sixteen units upward in the vertical direction. So on the side, let's just do a little rough sketch of what's going on. You have your X Square, multiply that by one over for that, makes it a flatter and then put the negative on the one over four that flips the graph about the X axis and then finally adding sixteen will just shift the latest graph upward by sixteen. So if we start off at the origin here when x zero, we see that we end up at sixteen and small rabbit, which is good and plugging a point or two. If you plug in one for X. Okay, you can see that you're getting something that's very close to sixteen now. Claudia, too. Then you're getting sixteen minus one fifteen. So that's a notable difference. And you can see here, by the way we've drawn the grids at this graph will look really flat, and we'LL come back and continue this after identifying the ex intercepts. But the Vertex we can already see it. The Vertex is just zero sixteen, which implies that the axis of symmetry is X equals zero. Now for the ex intercepts, as usual, just take your F set it equal to zero and softer X. So this will give you X squared people sixty four. And that means excess plus or minus eight. So this graph will not come down into the X axis until we're at eight or minus eight, some more or less from sketch here. So here's negative, eh? And plus eight. And there's a rough sketch of our function. F
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