Question

Determine whether the graph of y = 3x2 + 2x − 10 opens up or down and whether it has a maximum or minimum point.

Answer 1

Look at the coefficient of x^2 (for second degree functions only)
If it is positive, it opens up and hence a minimum.
If it is negative, it opens down and hence a maximum.

To find the vertex (max or minimum), complete the square:
\[y=3x^2+2x-10=3(x+1/3)^2-10-1/3\]
this means that the vertex is at (-1/3, -31/3)

Answer 2

thank you!