Start by expanding the brackets and simplifying the expression.
y=5x^2-x-1+(2x-1)^2y=5x2−x−1+(2x−1)2
y=5x^2-x-1+(4x^2-4x+1)y=5x2−x−1+(4x2−4x+1)
y=9x^2-5xy=9x2−5x
Take your simplified equation and complete the square.
y=9x^2-5xy=9x2−5x
y=9(x^2-5/9x+((5/9)/2)^2-((5/9)/2)^2)y=9⎛⎝x2−59x+(592)2−(592)2⎞⎠
y=9(x^2-5/9x+(5/18)^2-(5/18)^2)y=9(x2−59x+(518)2−(518)2)
y=9(x^2-5/9x+25/324-25/324)y=9(x2−59x+25324−25324)
y=9(x^2-5/9x+25/324)-(25/324*9)y=9(x2−59x+25324)−(25324⋅9)
y=9(x-5/18)^2-(25/color(red)cancelcolor(black)324^36*color(red)cancelcolor(black)9)
y=9(x-5/18)^2-25/36
Recall that the general equation of a quadratic equation written in vertex form is:
y=a(x-h)^2+k
where:
h=x-coordinate of the vertex
k=y-coordinate of the vertex
So in this case, the vertex is (5/18,-25/36).
