Chapter 8 - Review - Page 532: 53

Opens downward Vertex: $(-5/6, 73/12)$ x-intercepts: $(-2.3, 0)$, $(.6,0)$ y-intercept: $(0,4)$

$f(x) =-3x^2-5x+4$ The graph opens downward since the coefficient of $x^2$ is negative. $x=0$ $f(x) =-3x^2-5x+4$ $f(0) =-3*0^2-5*0+4$ $f(0)= -3*0-0+4$ $f(0)= 0+4$ $f(0)=4$ $(0,4)$ is the y-intercept. $a=-3$, $b=-5$, $c=4$ Vertex is at $x=-b/2a$ $x=-(-5)/2*-3$ $x=5/-6$ $x=-5/6$ $x=-5/6$ $f(x) =-3x^2-5x+4$ $f(-5/6) =-3(-5/6)^2-5*(-5/6)+4$ $f(-5/6) =-3*25/36 +25/6 +4$ $f(-5/6) = -25/12 +25/6 +4$ $f(-5/6) = -25/12 + 25*2/6*2 +4$ $f(-5/6) = -25/12+ 50/12 +4$ $f(-5/6) = 25/12 +4$ $f(-5/6) = 2 + 1/12 + 4$ $f(-5/6) = 6 + 1/12$ $f(-5/6) = 73/12$ $(-5/6, 73/12)$ is the vertex of the graph. $x=(-b±\sqrt {b^2-4ac})/2a$ $x=(-(-5)±\sqrt {(-5)^2-4*-3*4})/2*-3$ $x=(5±\sqrt {25+48})/-6$ $x=(5±\sqrt {73})/-6$ $x=(5±8.54)/-6$ $x=(5+8.54)/-6$ $x=13.54/-6$ $x=-2.25$ $x=-2.3$ $x=(5-8.54)/-6$ $x=-3.54/-6$ $x=.59$ $x=.6$ $(-2.3, 0)$ and $(.6, 0)$ are the x-intercepts