QuestionDetermine if the quadratic function has a max or min value, then find that value.
Studdy Solution
STEP 1
Assumptions1. The function is a quadratic function of the form . The coefficient of x^ (a) is positive
STEP 2
The standard form of a quadratic function is . If the coefficient of (a) is positive, the parabola opens upwards and the function has a minimum value. If the coefficient of (a) is negative, the parabola opens downwards and the function has a maximum value.
STEP 3
Looking at the given function , we can see that the coefficient of is3, which is positive. Therefore, the function has a minimum value.
STEP 4
To find the minimum value of the function, we need to find the vertex of the parabola. The x-coordinate of the vertex can be found using the formula .
STEP 5
Plug in the values for and into the formula to find the x-coordinate of the vertex.
STEP 6
Calculate the x-coordinate of the vertex.
STEP 7
Now that we have the x-coordinate of the vertex, we can find the y-coordinate by plugging into the function.
STEP 8
Calculate the y-coordinate of the vertex.
STEP 9
The vertex of the parabola is the point , and since the parabola opens upwards, the y-coordinate of the vertex is the minimum value of the function.
The function has a minimum value of .
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