# Question Video: Finding the Maximum or Minimum Value of a Quadratic Function Mathematics • 9th Grade

Find the maximum or minimum value of the function π(π₯) = π₯Β² + 10, given π₯ β [β3, 3].

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### 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, letβs decide if weβre dealing with the maximum or minimum. Weβre 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 weβre 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 ππ₯ squared plus ππ₯ 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 weβll 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.