Answer:
Vertex = (-2, -3)
Explanation:
The vertex of a parabola form
[tex]ax^2+bx+c[/tex]
is given by
[tex]x=-\frac{b}{2a}[/tex]Now, in our case a = 1, and b = 4; therefore, the vertex is
[tex]x=-\frac{4}{2(1)}[/tex][tex]x=-2[/tex]The x-coordinate of the vertex is x = -2 and now we find the y -coordinate.
The y-coordinate is given by substituting x = -2 into f(x) = x^2 + 4x + 1:
[tex]f(-2)=(-2)^2+4(-2)+1_{}_{}_{}[/tex][tex]f(-2)=4-8+1[/tex][tex]f(-2)=-3[/tex]The y-coordinate of the vertex is -3.
Hence, the coorindates of the vertex are x = -2 and x = -3 which can be written as (-2, -3).
