Question

Whixh statement is true about the graphs of the functions shown below?

Answer 1

Answer:

Step-by-step explanation:

Since G(0) = g(0) = 20, the parabolic graphs of these functions share a y-intercept:  (0, 20).

Completing the square puts these equations into vertex form, which simplifies comparisons of the graphs:

G(x) = 2x^2 - 12x + 20 becomes

          2(x^2 - 6x + 9 - 9) + 20, or

          2(x - 3)^2 - 18 + 20, or 2(x - 3)^2 + 2.  Comparing this result to

          a(x - h)^2 + k, we see that the vertex is located at (3, 2).

Going through the same process for g(x) 2x^2+12x+20, we get:

g(x) = 2(x + 3)^2 + 2, whose vertex is at (-3, 2).

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