Answer: [-12 , ∞)
Explanation:
To find the range of a parabola you would like the equation in the form y=ax²+bx+c, which is how it is given, to find the vertex.
From there you can use the equation x₁= -b/2a to find the x coordinate.
-(-8)/2(1) = 4.
Then you just plug the x₁ value into the original function to find the y-value.
y₁=(4)²-8(4)+4=16-32+4=-12
So we can conclude the vertex is (4,-12) and because the equation is a parabola that looks like a U, the y values or range, will start and -12 and go up to infinity. -12≤x or in interval notation [-12,∞).