https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/v/polynomial-intervals 2023-05-07T21:16:17.274254006Z Positive and negative intervals of polynomials If we know all the zeros of a polynomial, then we can determine the intervals over which the polynomial is positive and negative. This is because the polynomial has the same sign between consecutive zeros. So all we need to do is check each interval that is between two consecutive zeros (or before the smallest zero and after the largest zero). video https://cdn.kastatic.org/googleusercontent/BAJjD0IIO4PjJ1eQeT9NB94a8t9LH-ofsH3muj2vL4vR1en_l3RxM9rC87J_Z8Nq5iQgEeR8ZlKVKxLRmdTo8fpJUA Positive and negative intervals of polynomials If we know all the zeros of a polynomial, then we can determine the intervals over which the polynomial is positive and negative. This is because the polynomial has the same sign between consecutive zeros. So all we need to do is check each interval that is between two consecutive zeros (or before the smallest zero and after the largest zero). https://cdn.kastatic.org/ka-youtube-converted/z3faK7OV3Ew.mp4/z3faK7OV3Ew.mp4 520 Change in tandem https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:intervals-where-a-function-is-positive-negative-increasing-or-decreasing/v/increasing-decreasing-positive-and-negative-intervals 2021-05-05T14:53:16Z Increasing, decreasing, positive or negative intervals Function values can be positive or negative, and they can increase or decrease as the input increases. Here we introduce these basic properties of functions. video https://cdn.kastatic.org/googleusercontent/KeH1ZaAKr8tifSfCyQBg3KbdJ8WLhEvNRU-cWfp56Vjz8PpbDAWlHyhmMafXzMNAJSiLalC1tJpIeMk_lGjb9n_X Increasing, decreasing, positive or negative intervals Function values can be positive or negative, and they can increase or decrease as the input increases. Here we introduce these basic properties of functions. https://cdn.kastatic.org/ka-youtube-converted/KxOp3s9ottg.mp4/KxOp3s9ottg.mp4 356 Change in tandem https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/e/positive-and-negative-intervals-of-polynomials 2024-12-09T04:15:44.01032926Z Positive & negative intervals of polynomials Given a polynomial, determine the intervals in which it is positive or negative. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:intervals-where-a-function-is-positive-negative-increasing-or-decreasing/e/increasing-decreasing-intervals-of-functions 2025-08-29T01:00:50.274419509Z Increasing and decreasing intervals Highlight intervals on the domain of a function where it's only increasing or only decreasing. Sid Patel exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/a/positive-and-negative-intervals-of-polynomials 2023-02-11T00:49:50.919025829Z Positive & negative intervals of polynomials Learn about the relationship between the zeros of polynomials and the intervals over which they are positive or negative. article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/v/different-inputs-giving-same-value-for-function 2021-05-05T14:53:18Z Worked example: two inputs with the same output (graph) Sal finds the input value other than -5 for which f(x)=f(-5), given the graph of f. video https://cdn.kastatic.org/googleusercontent/T9LS6JQUy_PBE6C53by--XCd1rUoo_Pz9PjxNKZ_e6ajw46YGN7ddiigWDIbk_cgr6OWA50xSkyGDr18pMQ_6BIZ Worked example: two inputs with the same output (graph) Sal finds the input value other than -5 for which f(x)=f(-5), given the graph of f. https://cdn.kastatic.org/ka-youtube-converted/qSktOkaW6EA.mp4/qSktOkaW6EA.mp4 108 Change in tandem https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:inputs-and-outputs-of-a-function/e/match-inputs-to-outputs-from-a-graph 2026-04-07T23:17:37.123726494Z Function inputs & outputs: graph Find all the inputs that correspond to a given function output, using the function's graph. Tomer Gal exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/linear-nonlinear-functions-tut/e/interpreting-graphs-of-linear-and-nonlinear-functions 2026-06-12T17:50:45.743340147Z Interpret graphs of functions Interpret the graphs of both linear and nonlinear functions. ivan.savov exercise https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:change-in-tandem/v/interpreting-key-features-of-polynomial-graph-applications-precalculus-khan-academy 2025-08-28T00:00:48.862639845Z Interpreting key features of polynomial graph applications Interpret the meaning of key features on a transformed graph in a given context. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/718b9359-bf8e-4b83-8123-796c5e63390b_1280_720_base.png Interpreting key features of polynomial graph applications Interpret the meaning of key features on a transformed graph in a given context. https://cdn.kastatic.org/ka-youtube-converted/tPiJEFFHtg0.mp4/tPiJEFFHtg0.mp4 122 Change in tandem https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:change-in-tandem/e/applications-of-polynomial-graphs 2026-06-16T15:55:43.561813682Z Applications of polynomial graphs Interpret key features and make conclusions based off of the provided polynomial graphs. Courtney Chernin-Hitchings exercise