Find the x-intercepts (if any) for the graph of the quadratic function.
-$f ( x ) = x ^ { 2 } + 12 x + 15$ Give your answers in exact form.
A) $( - 6 \pm \sqrt { 21 } , 0 )$
B) $( 6 + \sqrt { 21 } , 0 )$
C) $( 6 \pm \sqrt { 15 } , 0 )$
D) $( - 12 \pm \sqrt { 15 } , 0 )$

Question

Quizplus · Accepted Answer

To find the x-intercepts of the quadratic function $f(x) = x^2 + 12x + 15$, we set $f(x) = 0$ and solve for $x$. Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 1$, $b = 12$, and $c = 15$, we find $x = \frac{-12 \pm \sqrt{(12)^2 - 4(1)(15)}}{2(1)} = \frac{-12 \pm \sqrt{144 - 60}}{2} = \frac{-12 \pm \sqrt{84}}{2} = -6 \pm \sqrt{21}$.

Find the X-Intercepts (If Any) for the Graph of the Quadratic