Question

Find the vertex and the y-intercept of the graph of y = –3x2 + 18x – 21.


     A. Vertex: (6,3); y-intercept: (0,–21)
  B. Vertex: (3,6); y-intercept: (0,–21)
  C. Vertex: (3,6); y-intercept: (0,21)
  D. Vertex: (6,3); y-intercept: (0,21)

Answer 1

$f(x)=ax^2+bx+c\\\\vertex\ (h;\ k)\ where\ h=\dfrac{-b}{2a}\ and\ k=f(h)$

$y=-3x^2+18x-21$

$a=-3,\ b=18,\ c=-21$

$Substitute:\\\\h=\dfrac{-18}{2(-3)}=\dfrac{-18}{-6}=3\\\\k=f(3)=-3(3^2)+18(3)-21=-3(9)+54-21=-27+54-21=6\\\\vertex\ (3,\ 6)\\\\y-intercept\ for\ x=0.\ Substitute:\\f(0)=-3(0^2)+18(0)-21=-21\\\\Answer:\ \boxed{B.\ Vertex:(3,\ 6);\ y-intercept:(0,-21)}$