Question

Determine whether the graph of y = 3x2 − 7x + 2 opens up or down and whether it has a maximum or minimum point. think the answer is maximum am I correct ?

Answer 1

The value of the coefficient of x² determines the way the parabola will be aligned.
If the coefficient of x² is positive:
the parabola is concave up (shaped like a 'U') and because of the 'U' shape, the function has a minimum point.

Answer 2

ok thanks

Answer 3

\[y=3\left( x ^{2}-\frac{ 7 }{ 3 } x+\left( \frac{ 7 }{ 6 } \right)^{2}-\left( \frac{ 7 }{ 6 } \right)^{2}\right)+2\]
\[y=3\left( x-\frac{ 7 }{ 6 } \right)^{2}-3*\frac{ 49 }{36 }+2\]
\[y+\frac{ 25 }{ 12 }=3\left( x-\frac{ 7 }{ 6 } \right)^{2}\]
\[\left( x-\frac{ 7 }{6 } \right)^{2}=\frac{ 1 }{ 3 }\left( y+\frac{ 25 }{12 } \right)\]
It is of the form
\[X ^{2}=4 a Y\]
It is an upward parabola with vertex
\[\left( \frac{ 7 }{6 },\frac{ -25 }{12 } \right)\]
this is the point of minima.