Find the range of the quadratic function.
\[
y=2 x^{2}-16 x+33
\]
Write your answer as an inequality using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer.
The range of the function is \(y \geq \boxed{1}\).
Step 1 :The range of a quadratic function is determined by its vertex and whether it opens upwards or downwards.
Step 2 :Since the coefficient of \(x^2\) is positive, the parabola opens upwards.
Step 3 :This means the vertex of the parabola is its minimum point.
Step 4 :The x-coordinate of the vertex of a parabola given by \(y=ax^2+bx+c\) is \(-\frac{b}{2a}\).
Step 5 :We can substitute this into the equation to find the y-coordinate of the vertex, which will be the minimum value of the function.
Step 6 :The range of the function will then be all values greater than or equal to this minimum value.
Step 7 :The range of the function is \(y \geq \boxed{1}\).