#color(magenta)("Depends on what is meant by 'evaluate'")#
#color(blue)("Simplifying the expression")#
Collecting like terms:
#(2x-16x)+(7y-4y)+(+3x^2)#
#-14x+3y+3x^2#
Order by degree (power that #x# is taken to)
#3x^2-14x+3y#
Set as equal to zero
#3x^2-14x+3y=0#
Subtract #3y# from both sides
#-3y=3x^2-14x#
Divide both sides by 3
#-y=3/3x^2-14/3 x#
Multiply by (-1)
#color(blue)(+y=-x^2+1/3x)" "color(magenta)("This may be as far as you need to go!")#
'~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the x-intercepts")#
At #x=0" "->" "y=-(0)^2+1/3(0) => y= 0#
Suppose we set #x=1/3#
Then #y=x^2+1/3x" "->" "y=0=(-1/3xx1/3)+(1/3xx1/3)#
#color(blue)(=> x_("intercepts")-> x= 0" and "x=1/3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine y intercept")#
Given that one of the x intercepts is at #x=0#
Then at #x=0# it is also the case that #y=0#
#=>color(blue)( y_("intercept")->y=0)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine vertex")#
Consider the standard form #" "y=ax^2+bx+c#
Write this as#" "y=a(x^2+b/ax)+c#
Then #x_("vertex")= (-1/2)xxb/a#
In your case #a=-1#
so #color(blue)(x_("vertex")=(-1/2)xxb -> (-1/2)xx-1/3 =+1/6)#
Substitute #x=1/6" in "y=-x^2+1/3x#
#color(blue)(=>y_("vertex")=-(1/6)^2+(1/3xx1/6)=1/18-1/36 = 1/36)#
#color(blue)("Vertex "->" "(x,y)=(1/6,1/36))#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
