Determine whether the quadratic function shown below has a minimum or maximum, then
determine the minimum or maximum value of the function.

Answer
The
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This quadratic function is in vertex form, , where is the vertex. Since the coefficient is positive, the parabola opens upwards, indicating that it has a minimum value. To find this minimum, we identify the vertex: and . Therefore, the minimum value of is at .

If you’re dealing with quadratic functions like this one, remember that the vertex is always your best friend! Often people forget to check the sign of the leading coefficient. A positive means a cheerful minimum (like the fun in this problem), while a negative leads to a gloomy maximum. Keep a t-chart handy, and don’t be shy about substituting values for sanity-checking your results!