MATH SOLVE

2 months ago

Q:
# Which of the following graphs is described by the function given below? y = 2x 2 + 6x + 3

Accepted Solution

A:

Answer:The graph in the attached figureStep-by-step explanation:we have[tex]y=2x^{2}+6x+3[/tex]This is the equation of a vertical parabola open upThe vertex is a minimumConvert to vertex formComplete squares[tex]y-3=2x^{2}+6x[/tex]Factor the leading coefficient[tex]y-3=2(x^{2}+3x)[/tex][tex]y-3+4.5=2(x^{2}+3x+2.25)[/tex][tex]y+1.5=2(x^{2}+3x+2.25)[/tex]Rewrite as perfect squares[tex]y+1.5=2(x+1.5)^{2}[/tex]The vertex is the point (-1.5,-1.5)Find the zeros of the functionFor y=0[tex]2(x+1.5)^{2}=1.5[/tex][tex](x+1.5)^{2}=3/4[/tex]square root both sides[tex]x+\frac{3}{2} =(+/-)\frac{\sqrt{3}}{2}[/tex][tex]x=-\frac{3}{2}(+/-)\frac{\sqrt{3}}{2}[/tex][tex]x=-\frac{3}{2}(+)\frac{\sqrt{3}}{2}=\frac{-3+\sqrt{3}}{2}=-0.634[/tex][tex]x=-\frac{3}{2}(-)\frac{\sqrt{3}}{2}=\frac{-3-\sqrt{3}}{2}=-2.366[/tex]Find the y-interceptFor x=0[tex]y=3[/tex]The y-intercept is the point (0,3)thereforeThe graph in the attached figure