Find the x- and y-intercepts. If no x-intercepts exist, state so.
-$$f ( x ) = 6 x ^ { 2 } + 12 x + 3$$
A) $\left( \frac { - 12 \pm \sqrt { 2 } } { 2 } , 0 \right) , ( 0,3 )$
B) $\left( \frac { - 2 \pm \sqrt { 2 } } { 2 } , 0 \right) , ( 0,3 )$
C) $\left( \frac { - 2 \pm \sqrt { 2 } } { 12 } , 0 \right) , ( 0 , - 3 )$
D) $\left( \frac { - 2 \pm \sqrt { 6 } } { 2 } , 0 \right\} , ( 0 , - 3 )$

Question

Quizplus · Accepted Answer

To find the x-intercepts, we need to set y = 0 and solve for x:
\begin{align*} 6x^2 + 12x + 3 &= 0 \ 2x^2 + 4x + 1 &= 0 \ (2x + 1)^2 &= 0 \end{align*}
So the only real solution is $x = -\frac{1}{2}$. This means the x-intercept is $\left(-\frac{1}{2},0\right)$. To find the y-intercept, we set x = 0:
$$f(0) = 3$$
So the y-intercept is $(0,3)$. The correct answer choice is B.

Find the X- and Y-Intercepts f(x)=6x2+12x+3f ( x ) = 6 x ^ { 2 } + 12 x + 3f(x)=6x2+12x+3

Find the X- and Y-Intercepts $f ( x ) = 6 x ^ { 2 } + 12 x + 3$