7th Problem 2016

Use the formula, -b/2 a to get the x coinage of the point. You will get -2/2 (3). Upon solving it, you get -1/3. You could plug this back into the equation to get the exact point, but there is only one answer choice with this x value, so you can select that option and be done.

The minimum point of the function is the vertex, as this function will graph out to be a parabola. To get the x value of the vertex, we must use the formula $x = -\frac {b}{2a}$ . We get $x = -\frac {2}{6} = -\frac {1}{3}$ . So the x value of the vertex would be $-\frac {1}{3}$ .

Then, we must plug in this x value into the whole function. We get: $y=3(-\frac { 1 }{ 3 } )^{ 2 }+2(-\frac { 1 }{ 3 } )+5 = 3(\frac {1}{9}) - 2(\frac {1}{3}) + 5 = \frac {1}{3} - \frac {2}{3} + 5 = \frac {5}{15} - \frac {10}{15} + \frac {75}{15} = -\frac {5}{15} + \frac {75}{15} = \frac {70}{15} = \frac {14}{3}$ . So the y value of the vertex is $\frac {14}{3}$ .

Note: I could have just stopped after finding the x value because that is the only $-\frac {1}{3}$ in the x value vertices in the answer choices. I decided to continue just to tell how you would solve to get the y value of the vertex.

The vertex of this parabola is $(-\frac {1}{3} , \frac {14}{3})$ .