Graphing Linear/Quadratic Equations April 18th, 2013

Warm Up 1) Write in set and interval notation: “The set of x such that x is greater than or equal to 5 or less than -2” Complete the tables for the equations & sketch the graphs: 2) f(x) = 3x - 2 3) f(x) = x2 - 5x + 6 X Y -1 1 2 3 X Y 1 2 3 4

Linear Equations To graph a linear equation put in slope intercept form: y = mx + b or f(x) = mx + b “m” represents the slope = rise/run “b” represents the y-intercept You can graph a linear equation by starting with the y-intercept. From this point use your slope to find the next point. If your slope is positive: go up, then to the right If you slope is negative: go down, then to the right

Examples Graph y = 5x - 3 Graph f(x) = -1/2x + 4

You Try! Graph f(x) = 2/3x - 2 Graph y = -x + 3

Review: Find the domain/range of the following graphs! Domain: Domain: Domain: Range: Range: Range: Most of the time for linear graphs the domain/range will be all real numbers, but you should look at your graph to see if there are any restrictions!

Quadratic Equations Standard Form: f(x) = ax2 + bx +c Quadratic equations come in two forms: Standard Form: f(x) = ax2 + bx +c Vertex Form: f(x) = a (x - h)2 + k

Quadratic Equations In standard form “C” is the y-intercept. (0, C) The x value of the vertex and the axis of symmetry can be found using x = –b 2a After you find the x-value of the vertex, plug in the equation to find the y-value. You can find the x-intercepts on the calculator, by factoring, or using the quadratic formula!

Examples Find the y-int/x-int(s), AOS, and vertex…GRAPH! f(x) = -x2 - 7x + 8 Domain: Range:

Examples Find the y-int/x-int(s), AOS, and vertex…GRAPH! F(x) = 4x2 – 6x + 1 Domain: Range:

You Try! Find the y-int/x-int(s), AOS, and vertex…GRAPH! f(x) = x2 – x + 6 Domain: Range:

Vertex Form: Horizontal Shift When a quadratic is in vertex form we can see the transformations! A horizontal shift occurs when adding (left) /subtracting(right) INSIDE of the parentheses: Parent Shifted f(x) = (x – 4)2

Vertex Form: Vertical Shift We can have both a horizontal and vertical shift! A vertical shift occurs when adding (up) /subtracting (down) OUTSIDE of the parentheses: f(x) = (x - 4)2 + 5 Parent f(x) = x2 Shifted

Examples List the transformations f(x) = (x + 7)2 - 8

Examples Graph the original function and the transformed graph, then list the transformations… f(x) = x2 f(x) = (x + 3)2 - 2

You Try! List the transformations f(x) = (x + 3)2 + 4

You Try Graph the original function and the transformed graph, then list the transformations… f(x) = x2 f(x) = (x + 5)2 - 4

Matching/Worksheet With the person next to you match the equation with the correct graph and the correct domain and range! You can use more than once. For the quadratic equations find all of the information and graph! Don’t forget Domain/Range

Homework Worksheet