ant of a quadratic Flashcards","topicId":"c8f64f78-0a93-4297-8bb4-31abc67a4490","topicSlug":"discriminant-of-a-quadratic","cards":[{"id":"62585547-e810-4a21-9a88-a815b2e6498c","cardType":"basic","front":"What happens to $ax^2+bx+c$ when $a=0$?","back":"$a\\neq0$; otherwise the $x^2$ term disappears and the function becomes linear.","points":1,"mcqOptions":null},{"id":"47b07295-fc00-4519-8a4c-21230e32437f","cardType":"basic","front":"What is a root of a quadratic?","back":"A value of $x$ for which $f(x)=0$.","points":1,"mcqOptions":null},{"id":"762b56fc-2eae-4717-8d23-88a39742aff6","cardType":"basic","front":"What do real roots represent on the graph of $y=f(x)$?","back":"The $x$-coordinates where the graph meets the $x$-axis.","points":1,"mcqOptions":null},{"id":"b8504e46-8a3b-4a0c-a9ce-b5d2945634be","cardType":"cloze","front":"For $ax^2+bx+c$, the discriminant is $\\text{[...]}$.","back":"For $ax^2+bx+c$, the discriminant is $\\boxed{\\Delta=b^2-4ac}$.","points":null,"mcqOptions":null},{"id":"5a226a95-ce3c-45f5-8d1b-d2bc9d1a4ad6","cardType":"basic","front":"What does $\u001b[?m\\Delta>0$ indicate about the roots?","back":"Two distinct real roots.","points":1,"mcqOptions":null},{"id":"255a601e-f6a2-417d-9293-47b545e93c6f","cardType":"basic","front":"What does $\\Delta=0$ indicate about the roots?","back":"One repeated real root, also called a double root.","points":1,"mcqOptions":null},{"id":"bf1432b3-1c35-4b98-a3bd-608575342a86","cardType":"basic","front":"What does $\\Delta<0$ indicate about the roots?","back":"No real roots, because $\\sqrt{\\Delta}$ is not real.","points":1,"mcqOptions":null},{"id":"dfb604c3-ac3a-4c6a-8ada-bdf7beb1e55e","cardType":"cloze","front":"When $\\Delta>0$, the graph [ ].","back":"When $\\Delta>0$, the graph crosses the $x$-axis twice.","points":null,"mcqOptions":null},{"id":"d1dac7c7-fadd-4c94-8b60-64f50d2ac1fb","cardType":"cloze","front":"When $\\Delta=0$, the graph [ ] at its turning point.","back":"When $\\Delta=0$, the graph touches the $x$-axis once at its turning point.","points":null,"mcqOptions":null},{"id":"bc840883-641f-4ee2-adda-e88d29737a48","cardType":"cloze","front":"When $\\Delta<0$, the graph [ ].","back":"When $\\Delta<0$, the graph does not meet the $x$-axis.","points":null,"mcqOptions":null},{"id":"7294a3b1-0506-4c14-b270-2f41440752b8","cardType":"basic","front":"How should a negative coefficient be handled when calculating $b^2$?","back":"Use $(-5)^2=25$, not $-5^2=-25$.","points":1,"mcqOptions":null},{"id":"ca831c6d-0c9a-4f26-ac78-e55da3faf298","cardType":"basic","front":"What is the repeated root when $\\Delta=0$?","back":"$x=\\frac{-b}{2a}$.","points":1,"mcqOptions":null},{"id":"01b69e5c-381a-448f-8811-8116fea16be1","cardType":"basic","front":"How can the discriminant determine intersections of $y=f(x)$ and $y=g(x)$?","back":"Set the two expressions for $y$ equal, then form a quadratic equation.","points":2,"mcqOptions":null},{"id":"1db86108-958d-4539-a49b-b6bfa34fa6c1","cardType":"cloze","front":"For a quadratic equation, “two distinct real roots” means $\\text{[...]}$.","back":"For a quadratic equation, “two distinct real roots” means $\\boxed{\\Delta>0}$.","points":null,"mcqOptions":null},{"id":"a7796b40-e7d3-4b67-ae74-32a42f4e7802","cardType":"cloze","front":"For a quadratic equation, “a repeated root” means $\\text{[...]}$.","back":"For a quadratic equation, “a repeated root” means $\\boxed{\\Delta=0}$.","points":null,"mcqOptions":null},{"id":"8ee17dd9-85a3-483b-85ea-74cdcf8dafcf","cardType":"cloze","front":"For a quadratic equation, “no real roots” means $\\text{[...]}$

1.2.5 Discriminant of a quadratic Flashcards

1.2.5 Discriminant of a quadratic Flashcards