Question 1168800


Write an equation in standard form of the parabola that has the same shape as the graph of
{{{f(x)= 4x^2 }}} or {{{g(x)=-4x^2}}}​, but with the given maximum or minimum.


given:

{{{Maximum=7}}} at {{{x=-2}}} => vertex is at ({{{-2}}},{{{7}}})=({{{h}}},{{{k}}}) =>{{{h=-2}}}, {{{k=7}}}

To move a parabola {{{h}}} units to the right, you would substitute {{{x- h}}} for {{{x}}}, and  to move up ad {{{k}}} units  in the corresponding quadratic equation

so, using {{{g(x)=-4x^2}}}

{{{g(x)=-4(x-h)^2+k}}} where {{{h=-2}}}, {{{k=7}}}

The equation in a standard form of the parabola that has a maximum at {{{f(x) = 7 }}}at {{{x=-2}}} is 

{{{f(x) =- 4(x -(- 2))^2 +7}}}

{{{f(x) = -4(x +2)^2 +7}}}


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(-2,7,.12),locate(-2,7,V(-2,7)),
 graph( 600, 600, -10, 10, -10, 10, -4(x +2)^2 +7)) }}}