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How do I sketch the graph y = (x^2 + 4*x + 2)/(3*x + 1)

This is an example of a rational function. So to sketch it, we need to know three things: 1) where it crosses the x and y axis 2) Where its turning points are, if it has any 3) Where its asymptotes are, if i...
AW
Answered by Alexander W. • Maths tutor
7659 Views

How do you solve an equation by completing the square?

Firstly, you can only complete the square on quadratic functions (functions in the form Ax 2 +Bx+C) If A=1, C onsider B, the coefficient of x. Substitute it into ( x + (B/2) ) 2 . We know if we multiply this...
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Answered by Emma J. • Maths tutor
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If y = 2^x, find dy/dx

Q: If y = 2^x, find dy/dx. ANSWER: 1) Take Logs of both sides of our equation y = 2^x So we get: log(y)=log(2^x) 2) Apply relevant log rule to rhs: Log rule: log(a^b) = b . log(a) [nb: the dot between b and ...
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Answered by Bav M. • Maths tutor
69628 Views

Polynomial long division, how do I do it?

Polynomial long division is how to divide long functions f(x), called the dividend, by another function g(x), called the divisor. Which could lead to having a remainder, if it doesn't divide perfectly. Lucki...
GP
Answered by Giulio P. • Maths tutor
7638 Views

Discriminants and determining the number of real roots of a quadratic equation

What is a discriminant? A discriminant is a value calculated from a quadratic equation. It use it to ' discriminate' between the roots (or solutions) of a quadratic equation. A quadratic equation is one of t...
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Answered by Gus N. • Maths tutor
412942 Views