shcards","topicId":"4d8eab55-3fc2-4d06-92e0-15ef2cd1ac4e","topicSlug":"algebra-and-functions-4","cards":[{"id":"77b4c962-3bdd-4b10-9d94-d689a7b04e9e","cardType":"basic","front":"For $f(x)=x^2-3x+2$, what is $f(4)$?","back":"$$f(4)=\\strong{6}$","points":1,"mcqOptions":null},{"id":"144285ca-f5f7-45e1-b38b-1b07c2065fc4","cardType":"cloze","front":"A quadratic has general form $\\text{[...]}$, where $a\\neq 0$.","back":"A quadratic has general form $\\boxed{f(x)=ax^2+bx+c}$, where $a\\neq 0$.","points":null,"mcqOptions":null},{"id":"f0260336-8e49-431c-965a-178619f5fdca","cardType":"cloze","front":"A quadratic has general form $f(x)=ax^2+bx+c$, where $\\text{[...]}$.","back":"A quadratic has general form $f(x)=ax^2+bx+c$, where $\\boxed{a\\neq 0}$.","points":null,"mcqOptions":null},{"id":"1ca5191e-4968-440c-a4ce-84b6000b2d3e","cardType":"basic","front":"What shape is the graph of a quadratic function?","back":"A smooth, symmetrical parabola.","points":1,"mcqOptions":null},{"id":"bc36a6bf-a2d6-4dae-9e70-dc51715088ed","cardType":"basic","front":"What are the turning point and axis of symmetry of $y=x^2$?","back":"

Turning point: $(0,0)$
Axis of symmetry: $x=0$

","points":2,"mcqOptions":null},{"id":"608b7224-abc0-4825-b7c7-1032d05d7783","cardType":"basic","front":"How does the sign of $a$ affect $y=ax^2+bx+c$?","back":"

$a>0$: opens upwards
$a<0$: opens downwards

","points":2,"mcqOptions":null},{"id":"8d4f5c95-b399-4396-80df-f5ab39675847","cardType":"basic","front":"How does $|a|$ affect a parabola's width compared with $y=x^2$?","back":"

$|a|>1$: narrower
$0<|a|<1$: wider

","points":2,"mcqOptions":null},{"id":"ffb88324-1c03-4bbb-81f5-984cd37ebca7","cardType":"basic","front":"What feature is read directly from $y=ax^2+bx+c$?","back":"The $y$-intercept is $(0,c)$.","points":1,"mcqOptions":null},{"id":"8a5c3af4-7445-4a59-aa7f-03f79e59dd33","cardType":"basic","front":"What features are read directly from $y=a(x-p)(x-q)$?","back":"The roots are $x=p$ and $x=q$.","points":1,"mcqOptions":null},{"id":"005e0d0e-ad3f-4815-8bae-25879674445b","cardType":"basic","front":"What root comes from the factor $(x+3)$?","back":"$x=-3$","points":1,"mcqOptions":null},{"id":"4b1c91b0-4e5b-494b-94d5-d764385451f0","cardType":"basic","front":"What features are read directly from $y=a(x-h)^2+k$?","back":"

Turning point: $(h,k)$
Axis of symmetry: $x=h$

","points":2,"mcqOptions":null},{"id":"d29bc890-135c-4c24-84fb-9ce5f92bdc1d","cardType":"basic","front":"Why is the turning point of $y=a(x-h)^2+k$ a minimum when $a>0$?","back":"Because $(x-h)^2\\geq 0$ and multiplying by $a>0$ preserves this.","points":2,"mcqOptions":null},{"id":"c1b9d102-bc93-48a8-a762-1cbfa1350c7e","cardType":"cloze","front":"The axis of symmetry of $y=ax^2+bx+c$ is $\\text{[...]}$. For roots $p$ and $q$, it is $x=\\frac{p+q}{2}$.","back":"The axis of symmetry of $y=ax^2+bx+c$ is $\\boxed{x=-\\frac{b}{2a}}$. For roots $p$ and $q$, it is $x=\\frac{p+q}{2}$.","points":null,"mcqOptions":null},{"id":"ec251bc3-0374-4181-86a2-5260eb5974b1","cardType":"cloze","front":"The axis of symmetry of $y=ax^2+bx+c$ is $x=-\\frac{b}{2a}$. For roots $p$ and $q$, it is $\\text{[...]}$.","back":"The axis of symmetry of $y=ax^2+bx+c$ is $x=-\\frac{b}{2a}$. For roots $p$ and $q$, it is $\\boxed{x=\\frac{p+q}{2}}$.","points":null,"mcqOptions":null},{"id":"f028d824-47c7-49a4-8a16-a8e1fc052b16","cardType":"basic","front":"How is the turning point found once its $x$-coordinate is known?","back":"Substitute the $x$-coordinate into the function.","points":1,"mcqOptions":null},{"id":"16378c15-98ef-4a18-b1ed-7db1088573ff","cardType":"basic","front":"What should be done first when completing the square if $a\\neq1$?","back":"Factor out $a$ from the terms involving $x$.","po

1.1.3 Algebra and functions Flashcards

1.1.3 Algebra and functions Flashcards