Question 927912
Did you remember the formula of:
{{{ f(x) = a(x-h)^2+k }}}
A vertex of this formula would be (h,k).
So we can plug in the vertex into this formula into:
{{{ f(x) = a(x-4)^2-1 }}}
We know that it passes through (2,3) so we can plug-in the x and y value into the formula also:
{{{ 3 = a(2-4)^2-1 }}}
And so we combine like terms now.
{{{ 3 = a(-2)^2-1 }}} Combine Like Terms
{{{ 3 = 4a-1 }}} Simplify
{{{ 3 + 1 = 4a-1+1 }}} Addition Property of Equality
{{{ 4/4 = 4a/4 }}} Division Property of Equality
{{{ 1 = a }}} Simplify
We know that a is one. So, into the formula we know that now.
{{{ f(x) = 1(x-4)^2-1 }}}
{{{ f(x) = (x-4)^2-1 }}} Distribution
{{{ f(x) = x^2-8x+16-1 }}} FOIL
{{{ f(x) = x^2-8x+15 }}} Simplify
{{{ y = x^2-8x+15 }}} We know that f(x) is y.