Question 668904

Parabolas are graphs with equations of the form {{{f(x)=ax^2+bx+c}}} where {{{a<>0}}}

The vertex of the parabola can provide us with information if parabola has the maximum or the minimum , so we need to be able to find its coordinates.

for any {{{y=ax^2+bx+c}}} we use the quadratic formula {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}},which could be written as {{{x = -b/2a +- (sqrt( b^2-4*a*c ))/2a }}}

then {{{x=-b/2a}}} will give us the {{{x-coordinate}}} of the vertex.  

We need only to find that coordinate, and then find the {{{y-coordinate}}} that goes with it by using that value for {{{x}}} in our equation for {{{f(x)}}}.


or

write equation in vertex form:

{{{y-k = m(x-h)^2}}}}

where ({{{h}}},{{{k}}}) are the vertex coordinates