Question 195118
9){{{y=2(x^2+1/2x)+3}}}
:
{{{y=2(x^2+1/2x+1/16)-1/8+3}}}
:
{{{y=2(x+1/4)^2+23/8}}}
:
equation with the form {{{y=ax^2}}}open up or down....if a postive it opens up and if a is negative opens down
:
since the vertex is at (-1/4,23,8) and lies above the x axis and a is positive meaning this parabola opens up then we know it doesnt cross the x axis.
:
{{{graph(300,300,-10,10,-10,10,2x^2+x+3)}}}
:
10) {{{y=3(x^2-4x+4)-12+12}}}
:
{{{y=3(x-2)^2}}}
:
since the vertex is at (2,0) and lies on x axis and a is positive meaning this parabola opens up then we know has only one point in common with the x axis and that point is (2,0)

{{{graph(300,300,-10,10,-10,10,3x^2-12x+12)}}}