Find the coordinates of the vertex and the intercepts of the quadratic function. When necessary, approximate the
x-intercepts to the nearest tenth.
-$$g ( x ) = 11 x ^ { 2 } + 264 x + 1463$$
A) $\mathrm { V } ( 264,1463 ) ; \mathrm { I } ( 0 , - 1463 ) ; ( - 24,0 ) ; ( 24,0 )$
B) $\mathrm { V } ( - 12 , - 121 ) ; \mathrm { I } ( 0,1463 ) ; ( - 15.3,0 ) ; ( - 8.7,0 )$
C) $\mathrm { V } ( 12 , - 121 ) ; \mathrm { I } ( 0 , - 1463 ) ; ( - 23,0 ) ; ( - 1,0 )$
D) $\mathrm { V } ( - 132 , - 121 ) ; \mathrm { I } ( 0,1463 ) ; ( 8.7,0 ) ; ( 15.3,0 )$

Question

Quizplus · Accepted Answer

The vertex of a quadratic function in the form $g(x) = ax^2 + bx + c$ can be found using the formula $(-b/2a, g(-b/2a))$. For $g(x) = 11x^2 + 264x + 1463$, the vertex is at $(-264/(2*11), g(-264/(2*11))) = (-12, -121)$. The y-intercept is found by evaluating $g(0)$, which gives $1463$. To find the x-intercepts, we solve $11x^2 + 264x + 1463 = 0$, which gives approximate solutions $x \approx -15.3$ and $x \approx -8.7$, using the quadratic formula.

Find the Coordinates of the Vertex and the Intercepts of the Quadratic