Linear and Quadratic Functions Chapter 8 Section 8.8

Objective Students will graph linear and quadratic functions

Vocabulary Linear function Quadratic function Parabola Minimum point Least value Maximum point Greatest value Axis of symmetry

Concept The function g defined by g(x) = 2x – 3 is called a linear function. If its domain is the set of all real numbers, then the straight line that is the graph of y = g(x) = 2x – 3 is the graph of g.

Concept A function f defined by f(x) = mx + b is a linear function. If the domain of f is the set of real numbers, then its graph is the straight line with slope m and y-intercept b.

Example Graph g(x) = 2x - 3

Concept A function f defined by f(x) = ax2 + bx + c is a quadratic function. If the domain of f is the set of real numbers, then the graph of f is a parabola

Concept When graphing quadratic functions the graph will not be a straight line it will be a curve or a parabola. A parabola either opens up or opens down, depending on the sign in front of ax2. Positive ax2 opens up, negative ax2 opens down

Concept If the parabola opens up it has a minimum point (or lowest point on the graph). The y-coordinate of this point is the least value of the function. If the parabola opens down it has a maximum point (highest point on the graph). The y-coordinate of this point is the greatest value of the function The minimum or maximum point of a parabola is called the vertex

Concept The vertical line that contains either the minimum point or the maximum point, is called the axis of symmetry of the parabola. If you fold the graph along the axis of symmetry, the two halves of the parabola coincide.

Concept The x-coordinate of the vertex of the parabola y = ax2 + bx + c is –b/2a. The axis of symmetry is the line x = -b/2a.

Concept When graphing a quadratic function you first find the axis of symmetry (x = -b/2a). Next you find the vertex point, which will be the y value using the x (axis of symmetry). Once you find the vertex point you will pick 2 points to the left and 2 points to the right of that point, make a table of values to find 4 other points, then plot the points in the coordinate plane and connect them forming a parabola.

Example Graph f(x) = x2 – 2x - 2

Example Graph f(x) = 2x2 + 4x - 3

Questions

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