topicId":"419fdf61-4e02-4a7d-b6c8-1b2bf3db974e","topicSlug":"quadratic-functions","cards":[{"id":"eb94a4af-ed16-478b-99b7-b70713d143a2","cardType":"cloze","front":"A quadratic function has the form [ ].","back":"A quadratic function has the form $f(x)=ax^2+bx+c$, where $a\\neq 0$.","points":null,"mcqOptions":null},{"id":"e2230a35-5b9c-45c6-b14a-3bccaadc365e","cardType":"basic","front":"If $a>0$ in $f(x)=ax^2+bx+c$, which way does the parabola open?","back":"It opens upwards.","points":1,"mcqOptions":null},{"id":"e5655b8b-d4d9-4e5b-b480-69c400d20b32","cardType":"basic","front":"If $a<0$, what type of turning point does the parabola have?","back":"A maximum point.","points":1,"mcqOptions":null},{"id":"ddd86c92-e70b-47f8-a230-e5183e2b21ae","cardType":"basic","front":"How does increasing $\\lvert a\\rvert$ affect a parabola?","back":"It becomes narrower and steeper.","points":2,"mcqOptions":null},{"id":"9cc14946-4bb3-43e6-be92-789bc9d7b8ab","cardType":"basic","front":"Where is the $y$-intercept of $f(x)=ax^2+bx+c$?","back":"At $(0,c)$.","points":1,"mcqOptions":null},{"id":"3b89bf49-e15b-46ea-84a4-2eb84c9ce3be","cardType":"cloze","front":"For $f(x)=a(x-p)(x-q)$, the roots are [ ].","back":"For $f(x)=a(x-p)(x-q)$, the roots are $x=p$ and $x=q$.","points":null,"mcqOptions":null},{"id":"e1c2cc8f-a929-4457-a24d-da67810a277e","cardType":"cloze","front":"For roots $x=p$ and $x=q$, the axis of symmetry is $\\text{[...]}$.","back":"For roots $x=p$ and $x=q$, the axis of symmetry is $\\boxed{x=\\frac{p+q}{2}}$.","points":null,"mcqOptions":null},{"id":"2b63cb30-958c-4a5a-98d4-a0a37e0f9d48","cardType":"basic","front":"What feature is read directly from $f(x)=a(x-h)^2+k$?","back":"The turning point $(h,k)$.","points":1,"mcqOptions":null},{"id":"399dc42a-4c82-4614-a6f0-55180d7bbfad","cardType":"basic","front":"What is the turning point of $f(x)=2(x+4)^2+1$?","back":"$(-4,1)$.","points":1,"mcqOptions":null},{"id":"5a6bd49c-2f8b-4791-b79e-7d7d95050803","cardType":"basic","front":"Find the axis of symmetry of $f(x)=(x-1)(x-5)$.","back":"$x=3$.","points":2,"mcqOptions":null},{"id":"4f5a183e-a61f-41c3-b3a0-cd6d06e0366c","cardType":"basic","front":"Find the turning point of $f(x)=(x-1)(x-5)$.","back":"$(3,-4)$.","points":2,"mcqOptions":null},{"id":"02ed3ccb-59fa-447b-aeae-fb0b88feec80","cardType":"basic","front":"Write $x^2-6x+5$ in completed-square form.","back":"$(x-3)^2-4$.","points":2,"mcqOptions":null},{"id":"1c2a2bf2-451e-402f-8cb1-dc29943600ae","cardType":"basic","front":"What is the minimum value of $x^2-6x+5$?","back":"The minimum is $-4$.","points":1,"mcqOptions":null},{"id":"b7753d0b-804b-4060-a316-8b7993141619","cardType":"cloze","front":"The solutions of $ax^2+bx+c=0$ are $\\text{[...]}$.","back":"The solutions of $ax^2+bx+c=0$ are $\\boxed{x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}}$.","points":null,"mcqOptions":null},{"id":"bf8b9f09-b7b8-40ec-9ddf-b82466ef7dd6","cardType":"basic","front":"What does $\\pm$ mean in the quadratic formula?","back":"Use both addition and subtraction.","points":1,"mcqOptions":null},{"id":"05458b32-520d-484e-9a1a-2190aa43f37f","cardType":"cloze","front":"For $ax^2+bx+c=0$, the discriminant is $\\text{[...]}$.","back":"For $ax^2+bx+c=0$, the discriminant is $\\boxed{\\Delta=b^2-4ac}$.","points":null,"mcqOptions":null},{"id":"5c59bbe9-cd77-4004-abf7-d0946c4e0f70","cardType":"basic","front":"What type of roots occur when $\\Delta>0$?","back":"Two distinct real roots.","points":1,"mcqOptions":null},{"id":"963eba3c-8dcf-4a1c-9145-4d

1.2.4 Quadratic functions Flashcards

1.2.4 Quadratic functions Flashcards