Q:

A parabola passes through the points (-2,8), (0,2), and (1,5). What function does the graph represent?

Accepted Solution

A:
ANSWER[tex]y = 2 {x}^{2} + x + 2[/tex]EXPLANATIONLet the function that represent the graph be:[tex]y = a {x}^{2} + bx + c[/tex]The parabola passes through the points (-2,8), (0,2), and (1,5). These points must satisfy the function.For (-2,8), we have [tex]8= a{( - 2)}^{2} + b( - 2) + c[/tex]This implies that that,[tex]4a - 2b + c = 8...(1)[/tex]For (0,2), we have,[tex]2= a{( 0)}^{2} + b( 0) + c[/tex]This implies that,[tex]c = 2[/tex]For (1,5), we have [tex]5= a{( 1)}^{2} + b( 1) + c[/tex]This implies that,[tex]a + b + c = 5...(2)[/tex]Put c=2 into equation (1) and (2).[tex]4a - 2b + 2 = 8[/tex][tex]4a - 2b = 8 - 2[/tex][tex]4a - 2b = 6[/tex][tex]2a - b = 3...(3)[/tex][tex]a + b + 2=5[/tex][tex]a + b =5 - 2[/tex][tex]a + b = 3...(4)[/tex]Add equation (3) and equation (4)[tex]3a = 6[/tex][tex]a = 2[/tex]Put a=2 into equation (4).[tex]2 + b = 3[/tex][tex]b = 3 - 2 = 1[/tex]Therefore the function is[tex]y = 2 {x}^{2} + x + 2[/tex]