Answer
Solution set as $x$-intercepts = $\{-\frac{3}{2},-5\}$
The graph of equation $y=2(x+2)^{2}+5(x+2)-3 $ is shown in Graph$(d)$
Work Step by Step
$y=2(x+2)^{2}+5(x+2)-3 $
To find $x$ -intercept, $y=0$
$2(x+2)^{2}+5(x+2)-3 =0$
Let $u= x+2$
$2u^{2}+5u-3 =0$
By factoring,
$2u^{2}+6u-u-3 =0$
$2u(u+3)-1(u+3) =0$
$(2u-1)(u+3) =0$
$(2u-1) =0$ or $(u+3) =0$
$u=\frac{1}{2}$ or $u=-3$
Let $u=\frac{1}{2}$
Replace $u$ with $x+2$
$x+2=\frac{1}{2}$
$x=\frac{1}{2}-2$
$x=-\frac{3}{2}$
Let $u=-3$
$x+2=-3$
$x=-3-2$
$x=-5$
Solution set as $x$-intercepts = $\{-\frac{3}{2},-5\}$
The graph of equation $y=2(x+2)^{2}+5(x+2)-3 $ is shown in Graph$(d)$
