Answer
Visually, the parabola intersects the x-axis in two points: $x=3$ and between $x=0$ and $x=-1$. Let's assume that $x=-\frac{1}{2}$. The x-intercepts are: $(3,0)$ and $(-\frac{1}{2},0)$
Algebraically: the x-intercepts are $(-\frac{1}{2},0)$ and $(3,0)$
Work Step by Step
$f(x)=0$
$-2x^2+5x+3=0~~$ ($a=-2,b=5,c=3$):
$x=\frac{-5±\sqrt {5^2-4(-2)(3)}}{2(-2)}=\frac{-5±\sqrt {49}}{-4}=\frac{-5±7}{-4}$
$x=\frac{2}{-4}=-\frac{1}{2}$ or $x=\frac{-12}{-4}=3$
x-intercepts: $(\frac{1}{2},0)$ and $(3,0)$
