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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
5741 Views

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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Find the roots of the equation y=x^2-8x+5 by completing the square.

Firstly, we need to look at completing the square. This is done by looking at the x^2-8x section of the equation. We need to find a way of converting it to the format of (x-a)^2. If you remember, when multip...
AG
Answered by Aaron G. • Maths tutor
4971 Views

Solve the equation " 2sec^2(x) = 5tanx " for 0 < x < π

Firstly, we must recognise that the equation contains two different trigonometric functions (sec() and tan()) and therefore we must rewrite one of these functions in terms of the other. Therefore we will nee...
JB
Answered by Joel B. • Maths tutor
15906 Views

Solve for 0<=θ<π, the equation sin3θ-(sqrt3)cosθ=0 (C2)

Rearrange the equation to give sin3θ=(sqrt3)cos3θ, then divide through by cos3θ to give sin3θ/cos3θ=sqrt3. We know from our trig identities that sinx/cosx=tanx, so our equation now becomes tan3θ=sqrt3. Use y...
BH
Answered by Becky H. • Maths tutor
9929 Views