Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions.
-$$\begin{array} { l }
f ( x ) = x ^ { 2 } - 12 x + 27 \
g ( x ) = 2 x ^ { 2 } - 12 x + 18
\end{array}$$
A) $x = 3 , x = - 3$
B) $x = \frac { 1 } { 3 } , x = - 3$
C) $x = - \frac { \sqrt { 10 } } { 2 } , x = \frac { \sqrt { 10 } } { 2 }$
D) $x = - \frac { \sqrt { 18 } } { 2 } , x = \frac { \sqrt { 18 } } { 2 }$

Question

Solve f(x) = g(x). Find the points of intersection of the graphs of the two functions.
-$$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 12 x + 27 \
g ( x ) = 2 x ^ { 2 } - 12 x + 18
\end{array}$$
A) $x = 3 , x = - 3$
B) $x = \frac { 1 } { 3 } , x = - 3$
C) $x = - \frac { \sqrt { 10 } } { 2 } , x = \frac { \sqrt { 10 } } { 2 }$
D) $x = - \frac { \sqrt { 18 } } { 2 } , x = \frac { \sqrt { 18 } } { 2 }$

Quizplus · Accepted Answer

To find the points of intersection, set $f(x) = g(x)$: $x^2 - 12x + 27 = 2x^2 - 12x + 18$. Simplifying gives $x^2 - 9 = 0$, which factors to $(x - 3)(x + 3) = 0$. Thus, $x = 3$ and $x = -3$.

Solve F(x) = G(x) f(x)=x2−12x+27g(x)=2x2−12x+18\begin{array} { l } f ( x ) = x ^ { 2 } - 12 x + 27 \\g ( x ) = 2 x ^ { 2 } - 12 x + 18\end{array}f(x)=x2−12x+27g(x)=2x2−12x+18​

Solve F(x) = G(x) $\begin{array} { l } f ( x ) = x ^ { 2 } - 12 x + 27 \\g ( x ) = 2 x ^ { 2 } - 12 x + 18\end{array}$