Question 469007

Quadratic functions in standard form

{{{f(x) = a(x - h)^2 + k }}}


{{{f(x)=(x^2)+14x+14}}}................complete the square to express the quadratic in standard form

{{{x^2+14x+14=0}}}

{{{x^2+14x=-14}}}.........Take half of the coefficient (don't forget the sign!) of the x-term, and square it. Add this square to both sides of the equation.

{{{x^2+14x+49=-14+49}}}

{{{(x+7)^2=35}}}

{{{(x+7)^2-35=0}}}

so, this is the standard form of a quadratic function with

{{{h = -7}}}

{{{k = -35}}}

{{{f(x)=(x+7)^2-35}}}



{{{ graph( 500, 500, -20, 20, -40, 20, x^2+14x+14) }}}