Question 118946
I always refer beck to the quadratic formula when
I have an axis of symmetry problem.The formula is:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
This finds the x-intercepts (roots)
when the equation is in the form {{{y = ax^2 + bx + c}}}
You can rewrite this formula as:
{{{x = -b/(2*a) +- sqrt( b^2-4*a*c )/(2*a) }}}
Think about what this says. It says " The axis of symmetry
is at {{{-b/(2*a)}}} and the roots are equally spaced on
either side, one on the minus side and one on the plus side
In the given equation, {{{2x^2 - 6Bx + 3}}}, {{{-6B}}}
represents {{{b}}} in the quadratic formula (I used "B" to avoid
confusion). {{{a = 2}}} is the other variable.
{{{-b/(2*a) = -(-6B)/(2*2)}}}
{{{-b/(2*a) = 6B/4}}}
The problem tells me this axis of symmetry is at {{{x=9}}}, so
{{{6B/4 = 9}}}
solve for {{{B}}}
{{{6B = 36}}}
{{{B = 6}}} answer
The equation turns out to be {{{y = 2x^2 -36x + 3}}}
I'll plot this
 {{{ graph( 600, 600, -5, 20, -200, 30, 2x^2 - 36x + 3) }}}
This shows the answer is OK