Reflection across the x-axis multiplies all y-values by -1, so g(x) = -f(x) = -x^2. The original parabola has vertex at (0,0), so in the form a(x-h)^2+k with integers a, h, k we have a = -1, h = 0, k = 0.
Thus: g(x) = -1(x-0)^2 + 0 = -(x-0)^2.
Find the reflection across the x-axis of f(x)=x^2 and write it in vertex form a(x–h)^2+k with integer a, h, k. Simple explanation and final expression.
Reflection across the x-axis multiplies all y-values by -1, so g(x) = -f(x) = -x^2. The original parabola has vertex at (0,0), so in the form a(x-h)^2+k with integers a, h, k we have a = -1, h = 0, k = 0.
Thus: g(x) = -1(x-0)^2 + 0 = -(x-0)^2.
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