Question

Identify the min/max and sketch this graph.
f(x)= 1/3x^2 - 10/3x +13/3
How do I solve this? Can you multiply it by three to make it easier, or can you not do that with function quadratics.

Answer 1

you could complete the square and put it in vertex form but it would probably be easier to use the fact that the x coordinate of the vertex is x = -b/2a or 10/3 divided by 2/3 or 5. So now we know that the vertex is (5, ), We can find the y value by putting 5 into the equation and finding y.

Answer 2

\[\frac{1}{3}(5)^2-\frac{10}{3}(5)+\frac{13}{3}=\frac{25-50+13}{3}=\frac{-12}{3}=-4\]

Answer 3

so we see that the vertex is (5,-4) and it is concave upward so it has a minimum.

Answer 4

Thank you for explaining it so well!

Answer 5

yw