Use the graph of the quadratic function $f (x) = a (x - h)^{2} + k$ to find the vertex, axis of symmetry, and the minimum or maximum value of the function.
The vertex is
(Type an ordered pair.)
The axis of symmetry is
(Type an equation.)
What is the minimum or maximum value of the function?

Answer

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Answer

So, the minimum or maximum value of the function is $k$ .

Steps

Step 1 ：The vertex of the quadratic function is given by the point $(h, k)$ .

Step 2 ：The axis of symmetry is a vertical line passing through the vertex, so its equation is $x = h$ .

Step 3 ：Since the coefficient of the $x^{2}$ term is $a$ , the parabola opens upwards if $a > 0$ and downwards if $a < 0$ .

Step 4 ：If the parabola opens upwards, the minimum value of the function is the $y$ -coordinate of the vertex, which is $k$ .

Step 5 ：If the parabola opens downwards, the maximum value of the function is the $y$ -coordinate of the vertex, which is $k$ .

Step 6 ：So, the minimum or maximum value of the function is $k$ .