Question

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In your own words, briefly define a quadratic function. The graph of the quadratic function f(x) = x2 is its own reflection across the y-axis. Give examples of at least two more functions that are their own reflection across the x-axis, the y-axis, or the line y = x without identifying which line you used for the line of reflection. The functions do not have to be quadratics. Respond to at least two of your classmates’ posts and identify what you think were the lines of reflection in their examples.

Answer 1

f(x) = ax2 + bx + c
The quadratic function comes in the form of the equation above. The quadratic function takes on the shape of a parabola with a vertex that can be determined by completing the square. Completing the square puts the quadratic function in the form:

y = a(x−h)2 + k
where the point (h, k) represents the vertex. The vertex is the turning point of the parabola. A line of symmetry passing through the vertex divides the parabola into two mirror image halves.

Answer 2

y = x^4 − 2x^2 + 1