How to answer these two questions ?
1 Answer
Explanation:
#(a)#
#"the equation of a parabola in "color(blue)"vertex form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#
where (h , k ) are the coordinates of the vertex and a is a constant.
#"the x-coordinate of the vertex is midway between the zeros"#
#rArrh=(0-4)/2=-2#
#rArrf(x)=a(x+2)^2-6#
#rArrp=k=-6#
#rArrcolor(magenta)"vertex "=(-2,-6)#
#"to find a use the point "(-4,0)" a point on the parabola"#
#"substitute into "f(x)=a(x+2)^2-6#
#0=4a-6rArra=6/4=3/2#
#(b)#
#"under a reflection in the x-axis"#
#• " a point "(x,y)to(x,-y)#
#rArr(-2,-6)to(-2,6)#
#"under reflection the parabola will now be maximum"#
#rArra=-3/2#
#rArrf(x)=-3/2(x+2)^2+6larrcolor(red)" in vertex form"#
#rArrf(x)=-3/2x^2-6xlarrcolor(red)" in terms of x"#
graph{(y-3/2x^2-6x)(y+3/2x^2+6x)=0 [-20, 20, -10, 10]}
