what is the vertex of $g(x)=-3x^{2}+18x + 2$?\n(3, -25)\n(-3, -25)\n(3, 29)\n(-3, 29)
what is the vertex of $g(x)=-3x^{2}+18x + 2$?\n(3, -25)\n(-3, -25)\n(3, 29)\n(-3, 29)
Answer
Answer:
C. $(3, 29)$
Explanation:
Step1: Find x - coordinate of vertex
For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex is given by $x=-\frac{b}{2a}$. Here $a=-3$ and $b = 18$. So $x=-\frac{18}{2\times(-3)}=\frac{-18}{-6}=3$.
Step2: Find y - coordinate of vertex
Substitute $x = 3$ into the function $g(x)=-3x^{2}+18x + 2$. Then $g(3)=-3\times3^{2}+18\times3 + 2=-3\times9 + 54+2=-27+54 + 2=29$. So the vertex is $(3,29)$.