### Video Transcript

Find the given maximum or minimum
value of the function π of π₯ equals π₯ squared plus 10 given that π₯ is contained
in negative three, three.

First, letβs decide if weβre
dealing with the maximum or minimum. Weβre given the function π of π₯
equals π₯ squared plus 10. Because we have a positive π₯
squared value, the parabola will open upwards. And that means weβre dealing with a
minimum value. The minimum value is found at this
vertex point that we label β, π.

To find the β-value, we solve for
negative π over two π when quadratic equations are in the form ππ₯ squared plus
ππ₯ plus π. We have π₯ squared plus 10, meaning
the π-value is zero and the π-value is one.

Plugging this in looks like this: β
equals negative zero over two times one. Zero divided by anything is
zero. β equals zero. The π-value will be equal to the
function of β. Our β-value is zero. And that means weβll solve for zero
squared plus 10. π equals 10.

Zero, 10 is the vertex, and it is
the minimum. And that means the minimum value is
10. The minimum outcome of our function
π of π₯ equals π₯ squared plus 10 has to be 10.