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What is 'completing the square' and how can I use it to find the minimum point of a quadratic curve?

Completing the square is a process used to put a quadratic curve into a particularly nice form. The form we want is y(x) = r(x+s)^2 + t for some numbers r,s, and t. A 'general' quadratic we would expect to b...
TP
Answered by Thomas P. • Maths tutor
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Intergrate ln(x) with resepct to x

To integrate this, we use the product rule. Think of it as intergrate [ 1 x ln (x)]. As by the product rule we chose one to intergrate and one to differentiate. We intergrate 1 to get x. We differentiate ln ...
LP
Answered by Leo P. • Maths tutor
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How do I multiply indices together?

Multiplying indices is much easier then it first seems. First you need to undertand what an index or power is, A^2 (A to the power of 2) means AxA, A^3 (A to the power of 3) means AxAxA and so on. The diffic...
FC
Answered by Freya C. • Maths tutor
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What is meant by 'the degree of a polynomial'?

The degree of a polynomial is the highest degree of the polynomials in your equation. For example, if you had (x^4 + 3x^2 + 5x), then the degree of the polynomial would be 4, as the largest polynomial in tha...
EH
Answered by Ellen H. • Maths tutor
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How do you complete the square? example: x^2 + 8x + 13=0

the method to complete the square is as follows; -take the constant (13) away from both sides of the equation leaving x and x^2 terms only on one side of the equation: x^2+8x=-13 -Add half of the value of th...
JM
Answered by John-Felipe M. • Maths tutor
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