ansion of a perfect square bracket is $(x+r)^2 = \\boxed{x^2+2rx+r^2}.","points":null},{"id":"863f4e18-f10c-4bb6-8c7b-eae036de488b","cardType":"basic","front":"When completing the square for $x^2 + px + q$, what constant value must be subtracted to correct the expression?","back":"The square of half the coefficient of $x$, or $\\left(\\frac{p}{2}\\right)^2$.","points":1},{"id":"87fb5ea1-e483-488e-a8a8-77cfdeec6b7a","cardType":"basic","front":"Complete the square for the expression $x^2 + 10x$.","back":"$$(x+5)^2 - 25$","points":1},{"id":"b85da8bb-b044-4fbf-8922-ac16eebc9671","cardType":"cloze","front":"For a quadratic in the form $y = (x+h)^2 + k$, the turning point (vertex) is $\\text{[...]}$.","back":"For a quadratic in the form $y = (x+h)^2 + k$, the turning point (vertex) is $\\boxed{(-h, k)}$.","points":null},{"id":"a2d9325c-d1f6-4f50-a820-c167d2f011ca","cardType":"basic","front":"If a quadratic is in the form $y = (x-4)^2 - 7$, what are the coordinates of the turning point?","back":"$$(4, -7)$","points":1},{"id":"ecd7d0d0-bd2f-48a3-901f-5c14b9a8b13b","cardType":"cloze","front":"A quadratic graph is a U-shaped curve called a [ ].","back":"A quadratic graph is a U-shaped curve called a parabola.","points":null},{"id":"af27a544-da19-4360-8b30-ee9adbc01b20","cardType":"basic","front":"How do you determine if a turning point is a maximum or a minimum from the completed square form $a(x+h)^2 + k$?","back":"

If $a$ is positive, it is a minimum.
If $a$ is negative, it is a maximum.

","points":2},{"id":"a44d3896-03df-4ee7-929f-ef771dac2f97","cardType":"basic","front":"When completing the square for $x^2 - 3x$, why is the correction constant $\\frac{9}{4}$?","back":"It is the square of half the coefficient: $\\left(-\\frac{3}{2}\\right)^2 = \\frac{9}{4}$.","points":2},{"id":"24e9c566-5b49-4823-b95e-320ce9bbf968","cardType":"basic","front":"What is the first step when completing the square for an expression where the $x^2$ coefficient is not 1 (e.g., $2x^2 + 16x$)?","back":"Factor out the leading coefficient from the $x^2$ and $x$ terms.","points":1},{"id":"f1a1b9ac-e5eb-4f35-9986-fbe64e99b73e","cardType":"cloze","front":"When completing the square for $2(x^2 + 8x)$, the internal correction is $-16$, but the total constant subtracted is $\\text{[...]}$ because of the outside multiplier.","back":"When completing the square for $2(x^2 + 8x)$, the internal correction is $-16$, but the total constant subtracted is $\\boxed{32}$ because of the outside multiplier.","points":null},{"id":"a3dce380-2550-4d79-9a0b-0be517b7f6c4","cardType":"cloze","front":"When completing the square for $2(x^2 + 8x)$, the internal correction is $-16$, but the total constant subtracted is $32$ because of the [ ].","back":"When completing the square for $2(x^2 + 8x)$, the internal correction is $-16$, but the total constant subtracted is $32$ because of the outside multiplier.","points":null},{"id":"9ca323b0-2744-467b-a267-8fca9e81b80c","cardType":"basic","front":"Outline the 4 steps to solve a quadratic equation by completing the square.","back":"

Complete the square.
Isolate the squared bracket.
Square root both sides (using $\\pm$).
Solve for $x$.

","points":3},{"id":"b830bf20-4851-4505-8350-7410613b8596","cardType":"basic","front":"What is surd form?","back":"Leaving a result as an exact root (e.g., $\\sqrt{6}$) instead of a rounded decimal.","points":1},{"id":"ca404fed-828b-41f8-972d-0c634a6ae6c1","cardType":"cloze","front":"When solving $(x+h)^2 = k$ by taking a square r

Completing the Square Flashcards

Completing the Square Flashcards

Completing the Square Flashcards

Completing the Square Flashcards