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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) = -\frac{1}{3} x^2 + 3x - 6 $

Vertex: $\left(\frac{9}{2}, \frac{3}{4}\right)$Axis of symmetry: $x=\frac{9}{2}$$x$ -intercepts: $(6,0),(3,0)$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

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In mathematics, the absolu…

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In Exercises 17-34, sketch…

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Okay, so we are discussing paralysis, and we need to find the Vertex, the axis of symmetries and the ex intercepts for the function F of X is equal to negative one third X squared, plus three eggs minus six. Okay, so the way we're going to solve this problem is first, we are going to write this in standard form. And then from standard form, we will find where the Vertex and the Ex intercepts and the axis of symmetry are. So tip ethicist. Okay. So to convert it to a standard form, let's pull out a negative one third. So the speed X squared plus nine x minus 18. Okay. And this gives us negative one third x squared. If we want to complete the square, this is plus nine x plus 9/2 squared minus 9/2. Squared minus 18 since gives us negative one third X minus nine over to squared plus 3/4. Recall that standard form is a times X minus age squared, plus K. And so the vertex is the point at H comma K. So here our Vertex is at nine over to calm a 3/4. So this is the Vertex. And then the axis of symmetry is that X equals eight. So the axis of symmetry is X equals nine over to and then to find the X intercept, let y equals zero and solve for X. So we have negative one third X minus 9/2 squared, plus 3/4 equals zero. So this gives us X minus nine over to is equal to 9/4. So this gives us the X is equal to sorry, X minus night over to is equal to Oh, excuse me. This is what happened. So this should be X minus nine over to squared. So now we need the square root of both sides. Sorry. So X minus 9/2 is equal to plus or minus three over to. So this means that X is equal to six or X is equal to three. So these are the X intercepts

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