Question 118946
Given {{{y = 2x^2-6bx+3}}}, find the value of b if the axis of symmetry is x = 9.
The axis of symmetry of a quadratic equation is given by: {{{x = -b/2a}}}.
The a and the b come from the general form of the equation: {{{y = ax^2+bx+c}}}
Since you are given the axis of symmetry as {{{x = 9}}}, you can write:
{{{x = -b/2a}}} Substituting a = 2 and b = -6b, and x = 9, you get:
{{{9 = -(-6b)/2(2)}}} Simplifying this:
{{{9 = 6b/4}}} Multiply both sides by 4.
{{{36 = 6b}}} Finally, divide both sides by 6.
{{{6 = b}}}...which matches your answer.