Find the x- and y-intercepts: $$y = 7 x ^ { 2 } + 5 x - 2$$
A) (1,0), $\left( \frac { 2 } { 7 } , 0 \right)$ ; (0,-2)
B) $\left( 1 , \frac { 2 } { 7 } \right)$ ; (0,-2)
C) (-1, 0), $\left( \frac { 2 } { 7 } , 0 \right)$ ; (0,2)
D) (-1,0), $\left( \frac { 2 } { 7 } , 0 \right)$ ; (0,-2)
E) (0,-1), $\left( 0 , \frac { 2 } { 7 } \right)$ ; (0,-2)

Question

Quizplus · Accepted Answer

To find the x-intercepts, we'll set $y=0$ and solve for $x$:

\begin{align*}
7x^2+5x-2&=0 \
(7x-2)(x+1)&=0 \
x&=-\frac17, \frac27
\end{align*}

So the x-intercepts are $\left(\frac27,0\right)$ and $\left(-\frac17,0\right)$.

To find the y-intercept, we'll set $x=0$:

$$y = 7\cdot0^2+5\cdot0-2 = -2$$

So the y-intercept is $(0,-2)$.

Therefore, the answer is $\boxed{\text{(D)}}$.

Find the X- and Y-Intercepts y=7x2+5x−2y = 7 x ^ { 2 } + 5 x - 2y=7x2+5x−2

Find the X- and Y-Intercepts $y = 7 x ^ { 2 } + 5 x - 2$