range the equation into standard form ($ax^2+bx+c=0$).","points":1},{"id":"2929c533-5e1d-4537-8e94-e647504d9421","cardType":"basic","front":"Why is the quadratic formula used instead of factorising?","back":"It works for any quadratic, including those with decimal or surd answers that do not factorise neatly.","points":1},{"id":"549e1665-c485-4b21-b6ef-d64746892f5a","cardType":"basic","front":"State the quadratic formula used to solve $ax^2+bx+c=0$.","back":"$$x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}$","points":1},{"id":"9b77f113-ef72-45ad-b9df-c53802e6490c","cardType":"cloze","front":"In the quadratic formula, the expression $\\text{[...]}$ is known as the discriminant.","back":"In the quadratic formula, the expression $\\boxed{b^2-4ac}$ is known as the discriminant.","points":null},{"id":"40dd1fbc-02fb-4961-b1bd-f0bb5ff421d0","cardType":"basic","front":"What are the coefficients $a$, $b$, and $c$ for the equation $5x^2=4x+7$?","back":"

$a=5$
$b=-4$
$c=-7$

","points":2},{"id":"15526ee1-d3ad-489b-81b6-c0e6abc125a7","cardType":"cloze","front":"The symbol $\\pm$ in the quadratic formula means [ ], which usually results in two solutions.","back":"The symbol $\\pm$ in the quadratic formula means plus or minus, which usually results in two solutions.","points":null},{"id":"7b7ac676-be15-4d94-a90c-defd4495dcd2","cardType":"basic","front":"Why should you write out the substitution step in an exam before using a calculator?","back":"To ensure you get method marks even if the final calculation is wrong.","points":1},{"id":"8c78a4c7-664b-4caa-9dad-96af1eac5b0c","cardType":"basic","front":"When solving a quadratic, at what stage should you round your answers?","back":"Only at the final step (do not round the square root halfway through).","points":1},{"id":"444b196c-d050-4f9a-89dc-30bda8145e47","cardType":"basic","front":"What is a surd?","back":"An exact square root that cannot be simplified to a whole number.","points":1},{"id":"ff38c25e-b812-42d9-b0b4-0f04e80760d8","cardType":"basic","front":"How do you simplify a surd like $\\sqrt{108}$?","back":"Find the largest square number that divides into it (e.g., $\\sqrt{36 \\times 3} = 6\\sqrt{3}$).","points":2},{"id":"2944670c-64c8-4d76-bef7-eb1bae991c36","cardType":"basic","front":"How do you give an exact answer for a quadratic equation?","back":"Leave the answer in surd form rather than converting to a decimal.","points":1},{"id":"fb3f18bc-bafa-49f8-be08-d9a8d4f356c6","cardType":"basic","front":"When solving for a length in a geometry problem, why might you reject one of the quadratic roots?","back":"Lengths cannot be negative; any root that results in a negative side length is invalid in context.","points":2},{"id":"5dd48e0a-5f55-45b8-831b-ad6e2deaf913","cardType":"basic","front":"How is Pythagoras' Theorem used to form a quadratic?","back":"Substitute side expressions into $a^2+b^2=c^2$ and expand/rearrange into $ax^2+bx+c=0$.","points":2},{"id":"c5692c14-a868-4b38-83dc-9d834a0a5b6d","cardType":"cloze","front":"To find significant figures, you must start counting from the [ ].","back":"To find significant figures, you must start counting from the first non-zero digit.","points":null},{"id":"ebc5d87b-2469-4e79-b581-ebe0b4df5b17","cardType":"basic","front":"If $x=\\frac{-10\\pm6\\sqrt{3}}{2}$, what is the simplified exact form?","back":"$$x=-5\\pm3\\sqrt{3}$","points":1},{"id":"08d22339-e874-4785-9147-1f953f5ef765","cardType":"basic","front":"What is the coefficient $b$ in the equation $x^2-x-9=0$?","back":"$$-1$","points":1},{"id":"b8b54369-f6c7-478f-adcf

Quadratic Formula Flashcards

Quadratic Formula Flashcards

Quadratic Formula Flashcards

Quadratic Formula Flashcards