Plot the points on the graph of f(x)=1/4(x+6)^2 −5 that correspond to x-values of −2 and −4. Then plot the vertex and the reflections of these points in the axis of symmetry.

Answer 1

The graph of f(x) = a(x - h)² + k is a parabola with vertex (h, k) and axis of symmetry the vertical line x = h.

So, the vertex for f(x) = (1/4)(x + 6)² - 5 is (-6, -5) and the axis of symmetry is x = -6.

f(-2) = -1 and f(-4) = -4, so the points (-2, -1) and (-4, -4) are on the graph.

The reflections of (-2, -1) and (-4, -4) in the line x = -6 are (-10, -1) and (-8, -4) respectively.