1 / 8

Graphing Inequalities

Learn how to graph quadratic inequalities of 2 variables using different methods. Understand how to shade regions and determine the solution by analyzing the graph.

Download Presentation

Graphing Inequalities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Graphing Inequalities Accelerated Geometry B/Algebra II A

  2. Quadratic Inequalities of 2 Variablesy > ax2 + bx + c or y > ax2 + bx + c • When graphing quadratic inequalities of 2 variables, first graph the quadratic function – • If the inequality has an “equal to” line under it, graph the function as is, but • If the inequality doesn’t have an “equal to” line under it, just sketch the function with a dotted line. • Then, since you want to graph all the points in which the y value is higher than the points on the graph, shade ABOVE the curve. Y > x2 – x - 6

  3. Quadratic Inequalities of 2 Variablesy < ax2 + bx + c or y <ax2 + bx + c • When graphing quadratic inequalities of 2 variables, first graph the quadratic function – • If the inequality has an “equal to” line under it, graph the function as is, but • If the inequality doesn’t have an “equal to” line under it, just sketch the function with a dotted line. • Then, since you want to graph all the points in which the y value is lower than the points on the graph, shade BELOW the curve. y < 4x2 – 3x - 2

  4. Graphing One-Variable Inequalitiesax2+ bx + c > 0 or ax2+ bx + c > 0 Way #1 – Use the number line • When graphing quadratic inequalities of 1 variable, first get the expression on one side of the inequality and 0 on the other. • Now factor the expression and find its roots. (In other words, find the values of x that make the expression equal 0.) • Plot those roots on the number line and write the factors to the side – but above the line. • Determine whether each factor will be positive or negative when numbers on the number line are substituted into the expression. • Remembering that factors are multiplied together to get the original expression, decide if the product will be positive or negative. • Shade the region corresponding to the positive product. • Write that region as an inequality. Solve x2 + 12 > 7x x2 – 7x + 12 > 0 (x – 3)(x – 4) > 0 x – 3 - - - - 0 + + + + + + + + x – 4 - - - - - - - - - -0 + + + + (x-3)(x-4) + + 3 - - - - 4 + + + so x > 4 or x < 3

  5. Graphing One-Variable Inequalitiesax2+ bx + c > 0 or ax2+ bx + c > 0 Way #2 – Use the function graph • When graphing quadratic inequalities of 1 variable, first get the expression on one side of the inequality and 0 on the other. • Now factor the expression and find its roots. (In other words, find the values of x that make the expression equal 0.) • Let the expression equal y and graph the function. • Determine where the y values on the graph are greater than 0. (In other words, where does the graph lie above the x axis?) The x values that correspond to this part of the graph is your solution. Solve x2 + 12 > 7x x2 – 7x + 12 > 0 (x – 3)(x – 4) > 0 Consider the graph of f(x) = (x – 3)(x – 4) 3 4 The graph is above the x axis to the left of 3 and to the right of 4, so x > 4 or x < 3

  6. Graphing One-Variable Inequalitiesax2+ bx + c < 0 or ax2+ bx + c < 0 Way #1 – Use the number line • When graphing quadratic inequalities of 1 variable, first get the expression on one side of the inequality and 0 on the other. • Now factor the expression and find its roots. (In other words, find the values of x that make the expression equal 0.) • Plot those roots on the number line and write the factors to the side – but above the line. • Determine whether each factor will be positive or negative when numbers on the number line are substituted into the expression. • Remembering that factors are multiplied together to get the original expression, decide if the product will be positive or negative. • Shade the region corresponding to the negative product. • Write that region as an inequality. Solve x2 + 12 > 7x x2 – 7x + 12 > 0 (x – 3)(x – 4) > 0 x – 3 - - - - 0 + + + + + + + + x – 4 - - - - - - - - - -0 + + + + (x-3)(x-4) + + 3 - - - - 4 + + + so 3 < x < 4

  7. Graphing One-Variable Inequalitiesax2+ bx + c < 0 or ax2+ bx + c < 0 Way #2 – Use the function graph • When graphing quadratic inequalities of 1 variable, first get the expression on one side of the inequality and 0 on the other. • Now factor the expression and find its roots. (In other words, find the values of x that make the expression equal 0.) • Let the expression equal y and graph the function. • Determine where the y values on the graph are less than 0. (In other words, where does the graph lie below the x axis?) The x values that correspond to this part of the graph is your solution. Solve x2 + 12 < 7x x2 – 7x + 12 < 0 (x – 3)(x – 4) < 0 Consider the graph of f(x) = (x – 3)(x – 4) 3 4 The graph is below the x axis between 3 and 4, 3 > x > 4

  8. Other Resources! http://www.purplemath.com/modules/ineqquad.htm http://www.mathwarehouse.com/quadratic-inequality/how-to-solve-and-graph-quadratic-inequality.php http://www.mathsisfun.com/algebra/inequality-quadratic-solving.html https://www.khanacademy.org/math/algebra2/polynomial-and-rational/quad_ineq/v/quadratic-inequalities?_escaped_fragment_=

More Related