If `y = 3x^2 + 6x + 2` is graphed in the xy-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

Options

A. y-coordinate of the vertex
B. x-intercept(s)
C. y-intercept
D. x-intercept of the line of symmetry

Answer

C

Explanation

Substituting 0 for x in the given equation yields `3(0)^2 + 6(0) + 2 = 2`. Therefore, the graph of the given equation passes through the point (0, 2), which is the y-intercept of the graph. The right-hand side of the given equation, `y = 3x^2 + 6x + 2`, displays the constant 2, which directly corresponds to the y-coordinate of the y-intercept of the graph of this equation in the xy-plane.
Choice A is incorrect. The y-coordinate of the vertex of the graph is −1, not 3, 6, or 2. Choice B is incorrect. The x-coordinates of the x-intercepts of the graph are at approximately −1.577 and −0.423, not 3, 6, or 2. Choice D is incorrect. The x-coordinate of the x-intercept of the line of symmetry is at −1, not 3, 6, or 2.