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))
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
![Tony B]()
Tony B
