Question 157349
{{{f(x)=(1/4)(x+7)^2+3}}} Start with the given function




{{{f(x)=(1/4)(x-(-7))^2+3}}} Rewrite {{{x+7}}} as {{{x-(-7)}}}



Notice how the equation is now in vertex form {{{f(x)=a(x-h)^2+k}}} where {{{a=1/4}}}, {{{h=-7}}} and {{{k=3}}}. Remember the vertex is (h,k). So the vertex is (-7,3). 



Since the Line of symmetry is simply vertical line through the x-coordinate of the vertex, this means that the Line of symmetry is {{{x=-7}}}



Remember, the max/min is ALWAYS at the vertex (since the vertex is the highest/lowest point). So the max/min value of f(x) is {{{f(x)=3}}}



Since we know that {{{a=1/4}}} this means that {{{a>0}}}. Since {{{a>0}}}, this means that the graph opens upward and there is a lowest point (which is the vertex). So the value f(-7)=3 is a minimum