Plot the points on the graph of f(x)=14(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

f(-2) = 14(-2+6)^2 -5 = 14(16)-5 = 224-5 = 219

f(-4)= 14(-4+6)^2-5= 14(4)-5 = 51

vertex = (-6, -5) as 14(x+6) -5 is in vertex form f(x)=a(x-h)+k with (h.k)= vertex

axis of symmetry is x=-6= the x coordinate of the vertex

(-2,219) reflected over x=-6 is (-10, 219)

(-4, 59) reflected is (-8, 59)

14(x+6)^2-5= 14x^2 + 14(12)x +14(36) -5= 14x^2+168x +504

-b/2a= -168/28=-6 =x is the axis of symmetry

Answer 2

To plot the points on the graph of f(x) = 14(x + 6)^2 - 5 that correspond to x-values of -2 and -4, we need to substitute these values into the equation and calculate the corresponding y-values:

f(-2) = 14(-2 + 6)^2 - 5 = 197 f(-4) = 14(-4 + 6)^2 - 5 = 109

So the two points are (-2, 197) and (-4, 109).

To plot the vertex of the parabola, we need to find the axis of symmetry, which is given by x = -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively. In this case, a = 14 and b = 0, so the axis of symmetry is x = -b/2a = 0. The vertex is located at the point (0, f(0)), where f(0) is the y-coordinate of the vertex:

f(0) = 14(0 + 6)^2 - 5 = 509

So the vertex is (0, 509).

To find the reflections of the points (-2, 197) and (-4, 109) in the axis of symmetry x = 0, we need to calculate the corresponding points on the other side of the parabola. The reflections will have the same y-coordinates as the original points, but their x-coordinates will be the negation of the original x-coordinates:

(-2, 197) reflects to (2, 197) (-4, 109) reflects to (4, 109)

Now we can plot all the points on the same graph: