Find the x- and y-intercepts of the function. $$p ( x ) = 3 x ^ { 2 } + 5 x - 3$$
A) $x$-intercepts: none; $y =$ intercept: $( 0 , - 3 )$
B) $x$-intercepts: $\left( \frac { - 5 - \sqrt { 61 } } { 6 } , 0 \right) , \left( \frac { - 5 + \sqrt { 61 } } { 6 } , 0 \right) ; y =$ intercept: $( 0 , - 5 )$
C) $x$-intercepts: $\left( \frac { - 5 - \sqrt { 61 } } { 6 } , 0 \right) , \left( \frac { - 5 + \sqrt { 61 } } { 6 } , 0 \right) ; y = \operatorname { intercept } : ( 0 , - 3 )$
D) $x$-intercepts: none; $y =$ intercept: $( 0,5 )$

Question

Quizplus · Accepted Answer

To find the x-intercepts, set $p(x) = 0$ and solve for $x$. Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 3$, $b = 5$, and $c = -3$, we find the x-intercepts as given in option C. The y-intercept is found by setting $x = 0$, which gives $p(0) = -3$, thus the y-intercept is $(0, -3)$.

Find the X- and Y-Intercepts of the Function p(x)=3x2+5x−3p ( x ) = 3 x ^ { 2 } + 5 x - 3p(x)=3x2+5x−3

Find the X- and Y-Intercepts of the Function $p ( x ) = 3 x ^ { 2 } + 5 x - 3$