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

Find the maximum or minimum value of the function ๐‘“(๐‘ฅ) = ๐‘ฅยฒ + 10, given ๐‘ฅ โˆˆ [โˆ’3, 3].

01:55

Video Transcript

Find the given maximum or minimum value of the function ๐‘“ of ๐‘ฅ equals ๐‘ฅ squared plus 10 given that ๐‘ฅ is contained in negative three, three.

First, letโ€™s decide if weโ€™re dealing with the maximum or minimum. Weโ€™re given the function ๐‘“ of ๐‘ฅ equals ๐‘ฅ squared plus 10. Because we have a positive ๐‘ฅ squared value, the parabola will open upwards. And that means weโ€™re dealing with a minimum value. The minimum value is found at this vertex point that we label โ„Ž, ๐‘˜.

To find the โ„Ž-value, we solve for negative ๐‘ over two ๐‘Ž when quadratic equations are in the form ๐‘Ž๐‘ฅ squared plus ๐‘๐‘ฅ plus ๐‘. We have ๐‘ฅ squared plus 10, meaning the ๐‘-value is zero and the ๐‘Ž-value is one.

Plugging this in looks like this: โ„Ž equals negative zero over two times one. Zero divided by anything is zero. โ„Ž equals zero. The ๐‘˜-value will be equal to the function of โ„Ž. Our โ„Ž-value is zero. And that means weโ€™ll solve for zero squared plus 10. ๐‘˜ 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 ๐‘“ of ๐‘ฅ equals ๐‘ฅ squared plus 10 has to be 10.

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