Can you help me solve

Question

1÷4+6÷y+2=6÷y Use quadratic formula and simplify

 

B=3abx²-5x solve for x

 

p(x) = -x² - 8x - 12 find vertex, Y intercept and X interxept and graph

Answer 1

(1) 1/4+6/(y+2)=6/y, multiply through by 4y(y+2):

y(y+2)+24y=24(y+2),

y²+2y+24y=24y+48,

y²+2y-48=0=(y+8)(y-6) so y=-8 or 6.

(2) b=3abx²-5x,

3abx²-5x-b=0. Applying the formula:

x=(5±√(25+12ab²))/(6ab).

(3) p(x)=-x²-8x-12=-(x²+8x+12)=-(x²+8x+16-4) or -(x+2)(x+6),

p(x)=-((x+4)²-4)=4-(x+4)². The right-hand side has a maximum value of 4 when x=-4, so the vertex is at (-4,4), and the graph is an upside down parabola. x-intercept is when y=p(x)=0=-(x+2)(x+6). 2 x-intercepts: (-2,0) and (-6,0). y-intercept when x=0 so (0,-12) is the y-intercept.