Let g(x) be the reflection of f(x) = x² + 3 on the x-axis. What is the function rule for g(x)?

Solution:

Every parabola has:

a vertex

an axis of symmetry 

a maximum OR minimum value

Y-intercept.

f(x) = x² + 3 is a concave up parabola, the vertex is (0,3) and the axis of symmetry is the x axis (x=0)

To reflect a graph, f(x) over the x-axis, you take -f(x).

If it is reflected in the y axis it will stay the same so g(x) = x² + 3

If it is reflected in the x axis (about y=0) then it will still have the y axis as the axis of symmetry but it will be concave down and the vertex will be (0,-3)

so g(x) = -x² - 3

Let g(x) be the reflection of f(x) = x² + 3 on the x-axis. What is the function rule for g(x)?

Summary:

If it is reflected in the y axis it will stay the same so g(x) = x² + 3. If it is reflected in the x axis (about y = 0) then it will still have the y axis as the axis of symmetry but it will be concave down and the vertex will be (0, -3) so   g(x)= - x² - 3