Answer:
-4 ≤ y < ∞
Explanation:
You want the range of the relation y = x² -8x +12.
Range
The range is the vertical extent of the graph. We recognize the graph will be a parabola that opens upward (the leading coefficient of the quadratic is positive). The range will extend to positive infinity.
The lower limit of the range will be the y-value of the vertex of the parabola. We can find that by rewriting the equation in vertex form.
y = (x² -8x) +12
y = (x² -8x +16) +12 -16
y = (x -4)² -4
Comparing this to the vertex form equation ...
y = (x -h)² +k . . . . . . . . . vertex (h, k)
we see that k = -4. The minimum value of y is -4, so ...
the range is -4 ≤ y < ∞
__
Additional comment
In interval notation, this is [-4, ∞). This could also be written as y ≥ -4.
<95141404393>