Question 1205875


Select all the true statements for the quadratic function

{{{f(x) = 5x^2 + 70x + 245}}}

write in vertex form {{{f(x) = a(x-h)^2 + k }}}, where {{{h}}} and {{{k}}} are {{{x }}}and {{{y }}}coordinates of vertex

complete square

{{{f(x) = 5(x^2 + 14x) + 245}}}

{{{f(x) = 5(x^2 + 14x+b^2)-5b^2 + 245}}}......{{{b=14/2=7}}}

{{{f(x) = 5(x^2 + 14x+7^2)-5*7^2 + 245}}}

{{{f(x) = 5(x +7)^2-245 + 245}}}

{{{f(x) = 5(x +7)^2}}}

=> {{{h=-7}}}, {{{k=0}}}

answer: all the true statements are

B. The vertex of the function is at ({{{-7}}}, {{{0}}}).=>{{{true}}}

D. The function is decreasing when {{{-infinity < x < -7}}}.=>{{{true}}}

E. The range of the function is all positive real numbers including zero.=>{{{true}}}


{{{ graph( 600, 600, -10, 10, -10, 10, 5(x +7)^2) }}}