Question 111874

Determine whether the graph of each parabola opens upward or downward. 

We know that: 


quadratic function is 

{{{y = f(x) = ax^2 + bx + c}}}, 

and its graph is a{{{ parabola}}}


If {{{a > 0}}}, it opens {{{upward}}}

If {{{a < 0}}}, it opens {{{downward}}}


your parabola is:

{{{y=-(1/2)x^2+3 }}}


As you can see {{{a = -1/2}}} , that means {{{a < 0}}}}; consequently, your parabola opens {{{downward}}}

Are the ordered pairs x=-3 and 2 1/2 and y=3 and -10?


ordered pairs ({{{x}}} , {{{y}}}) are : ({{{-3}}} , {{{3}}}) and ({{{2 (1/2)}}}, {{{-10}}})



{{{y=-(1/2)x^2+3 }}}…………evaluating our function for ({{{-3}}} , {{{3}}}) 


{{{3 = -(1/2)*3^2 + 3}}}

{{{3 = -9/2 + 3}}}

{{{3*2 = -9*2/2 + 3*2}}}………….. multiply both sides by {{{2}}}

{{{6 = -9 + 6}}}

{{{6 =  -3}}}

{{{y=-(1/2)x^2+3 }}}………… and for ({{{2(1/2)=5/2)}}}, {{{-10}}})

{{{-10=-1/2(5/2)^2+3 }}}

{{{-10 = -(1/2)(25/4) + 3 }}}…………

{{{-10 = -25/8 + 3 }}}………… multiply both sides by {{{8}}}

{{{-80 = -25 + 24 }}}…………

{{{-80 = - 1 }}}…………

ordered pairs ({{{-3}}} , {{{3}}}) and ({{{2 (1/2)}}}, {{{-10}}}) are not on the graph of the function


*[invoke solve_quadratic_equation -1/2, 0, 3]