Q: What is the reflection of f of x equals x2 across the x axis?

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The question asks about "these functions". In those circumstances would it be too much to expect that you make sure that there is something that these can refer to?

It is a parabola which doesn't touch the X-axis. i.e., It has no real roots.

y=x2-4x+4 y = (x-2)(x-2) x=2 the graph only crosses the x-axis at positive 2. this is the minimum of the graph and the only point that is crosses the x-axis.

y = x2 is an (approximately) U shaped graph that is entirely above the x axis and is symmetric about the y axis. y = x3 is asymptotically negatively infinite when x is negatively infinite and positively infinite when x is positively infinite. It is symmetric about the line x+y=0.

y=x2+2x+1 -b -2 2a= 2= -1 = axis of symmetry is negative one.

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The question asks about "these functions". In those circumstances would it be too much to expect that you make sure that there is something that these can refer to?

y = x2 + 4 The graph is a parabola, with its nose at y=4 on the y-axis, and opening upward.

If a function reflects along the x-axis, that indicates that it has both negative and positive solutions. For example, y = x2 reflects along the x-axis because x2 = -x2. In general, a function will reflect along the x-axis if f(x) = f(-x).

It is a parabola which doesn't touch the X-axis. i.e., It has no real roots.

If you mean x2-3x+5 then the answer is none because its discriminant is less than zero

Line of symmetry: x = 3

x2 + y - 52 = 30x2 - x2 + y - 52 + 52 = - x2 + 30 + 52y = -x2 + 82Since a = -1, the parabola open downward, and crosses the x-axis at x = +&- sq.root of 82.0 = -x2 + 820 - 82 = -x2 + 82 - 82-82 = -x282 = x2+&- sq.root of 82 = x

x2 + x2 = 2x2

y = x2 + 8x - 7 a = 1, b = 8, c = -7 the equation of the axis of symmetry: x = -b/2a x = -8/(2*1) = -4

No real roots. Imaginary roots as this function does not intersect the X axis.

y=x2-4x+4 y = (x-2)(x-2) x=2 the graph only crosses the x-axis at positive 2. this is the minimum of the graph and the only point that is crosses the x-axis.

y = x2 is an (approximately) U shaped graph that is entirely above the x axis and is symmetric about the y axis. y = x3 is asymptotically negatively infinite when x is negatively infinite and positively infinite when x is positively infinite. It is symmetric about the line x+y=0.