Find the Vertex of the function glven below?y = x^2-4x+1

Accepted Solution

Answer:The vertex of the function is (2, -3).Step-by-step explanation:Given:[tex]y=x^{2}-4x+1[/tex]So, to find the vertex of the function we will get the equation in the form:[tex]y=ax^{2} +bx+c[/tex][tex]y=1x^{2}+(-4)x+1[/tex]So, [tex]a=1,b=-4,c=1[/tex]Then, we calculate the x-coordinate of the vertex:[tex]x=\frac{-b}{2a}[/tex][tex]x=\frac{-(-4)}{2\times1}\\x=\frac{4}{2}[/tex][tex]x=2[/tex]And now, we get the [tex]y[/tex] value of vertex of the function:[tex]y=1x^{2}-4x+1[/tex][tex]y=1\times 2^{2}+(-4)\times (2)+1[/tex][tex]y=1\times 4-8+1[/tex] (when the opposite signs multiply the result is negative)[tex]y=4-8+1[/tex][tex]y=-3[/tex]Therefore, the vertex is at [tex](x,y)=(2,-3)[/tex].