Given the function f ( x ) = 3 x 2 − 7 x + 7 . Calculate the following values: f ( − 2 ) = f ( − 1 ) = f ( 0 ) = f ( 1 ) = f ( 2 ) =

Answer 1

f(-2) =3(4)+7(2)+7 =33

f(-1) =3 +7+7 = 17

f(0) = 7

f(1) = 3-7+7 = 3

f(2) =3(4) -7(2) + 7= 5

f(3) =3(9)-7(3) +7 = 13

3x^2-7x + 7=0

x=7/6 + or - (1/6)sqr(49-4(3)(7)), the discriminate <0 so there are no x intercepts, the axis of symmetry is x=7/6

the vertex has an x coordinate of 7/6

plug that into the trinomial to get the y coordinate of the vertex

3(7/6)^2 -7(7/6) + 7= 49/12 - 49/6 + 42/6 = 49/12 -14/12 = 35/12 = 2 11/12

the vertex or minimum point is (7/6, 35/12) It's an upward opening parabola