Answer
(a) See graph, opens down, vertex $(-\frac{3}{4},\frac{17}{4})$, axis of symmetry $x=-\frac{3}{4}$, y-intercept $(0,2)$, x-intercept(s) $(-1.78,0),(0.28,0)$.
(b) domain $(-\infty,\infty)$, range $(-\infty,\frac{17}{4}]$.
(c) decreasing on $(-\frac{3}{4},\infty)$, increasing on $(-\infty,-\frac{3}{4})$.
Work Step by Step
(a) See graph for $y=-4x^2-6x+2=-4(x+\frac{3}{4})^2+\frac{17}{4}$, we can find that the graph opens down, vertex $(-\frac{3}{4},\frac{17}{4})$, axis of symmetry $x=-\frac{3}{4}$, y-intercept $(0,2)$, x-intercept(s) $(-1.78,0),(0.28,0)$.
(b) We can determine the domain $(-\infty,\infty)$, range $(-\infty,\frac{17}{4}]$.
(c) The function is decreasing on $(-\frac{3}{4},\infty)$, increasing on $(-\infty,-\frac{3}{4})$.
