Question 739816

what is the x-intercepts when the vertex is ({{{1}}},{{{20}}}) and y-intercept is ({{{0}}},{{{16}}})

With coordinates of vertex given, equation can be written as follows:

{{{y=(x-1)^2-20}}}

To find the {{{x-intercepts}}}, set {{{y=0}}} and solve for {{{x}}}:

{{{0=(x-1)^2-20}}}

{{{(x-1)^2=20}}} take sqrt of both sides

{{{sqrt((x-1)^2)=sqrt(20)}}}


{{{x-1=4.47}}} 

{{{x=4.47+1}}} 

{{{x=5.47}}} 

or 

{{{-(x-1)=4.47}}}

{{{-x+1=4.47}}}=> {{{-4.47+1=x}}}

{{{x=-3.47}}}



{{{ graph( 600, 600, -10, 10, -30, 10, (x-1)^2-20) }}}