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This method is known as completing the square. To find the constant a, we must halve the coefficient of x, which in this case is 4. This is to compensate for the double term when expanding the brackets. S...

a) y = x² + 3x + 1b) y = 2x + 3At points of intersection (a) = (b).2x + 3 = x ² + 3x + 1Note this is a quadratic expression which will solve for 2 unique solutions, providing the dis...

To find the inverse of a function, f^-1(x):1) set f(x) as y: y =  (2x + 3)/(x - 4)2) swap x and y: x = (2y + 3)/(y -4)3) solve the new equation for y: x(y -4) = 2y + 3 = xy -4x2y - xy = -4x - 3y...

a) First deduce that problem can be solved by inspection. Then use the fact that the derivative of tan3x equals 3sec^2(3x) and adjust for the constant. (Note this fact should be given in a formula booklet...

We solve inequalities exactly like normal equations except for Dividing by a Negative Coefficient where we Change the inequality directionE.gx+2>4 is ... x>2 (ask second ...