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Creating a Difference-Quotient and Simplifying
281–290 Given f(x), find the difference-quotient
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Evaluating Piecewise Functions for Particular Inputs
291–300 Given the piecewise function, evaluate as requested.
291. Evaluate f(1) in
292. Evaluate f(-1) in
293. Evaluate f(2) in
294. Evaluate f(0) in
295. Evaluate f(–1) in
296. Evaluate f(–4) in
297. Evaluate f(–5) in
298. Evaluate f(51) in
299. Evaluate f(0) in
300. Evaluate f(4) in
Chapter 6
Quadratic Functions and Relations
A quadratic function is created from a quadratic expression — an expression with a variable raised to the second power. The graphs of quadratic functions look like U-shaped curves that open upward or downward. A quadratic relation may open left or right. The key to graphing a quadratic function or relation is to find its vertex, determine which way it opens, and find a point or two that can be used to sketch the curve.
The Problems You’ll Work On
In this chapter, you’ll work with quadratic curves in the following ways:
Determining the vertex and intercepts from the function rule
Rewriting quadratic functions in the standard form for a parabola
Sketching the graphs of parabolas
Using quadratic functions and their properties to solve applications
What to Watch Out For
Don’t let common mistakes trip you up; watch for the following when working with quadratic curves:
Finding the opposite of the coefficient of b when solving for the coordinates of the vertex
Watching for the correct direction of the parabola’s opening when sketching
Performing completing the square correctly when rewriting the parabola’s equation in standard form
Using the correct property of a parabola when solving an application
Determining the Vertex and Intercepts of a Parabola
301–310 Find the intercept(s) and vertex of the parabola.
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