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

SAT · Math · previous-year question

  1. A.$y$-coordinate of the vertex
  2. B.$x$-intercept $(\mathrm{s})$
  3. C.$y$-interceptcorrect
  4. D.$x$-intercept of the line of symmetry

Answer

C. $y$-intercept

Explanation

Choice $\mathbf{C}$ is correct. 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, $y=3 x^{2}+6 x+2$, displays the constant 2 , which directly corresponds to the $y$-coordinate of the $y$-intercept of the graph of this equation in the $x y$-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

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