Find the axis of symmetry y=-x^2-4x+1 explain with x
To find the axis of symmetry for the quadratic equation y=-x^2-4x+1, we first need to complete the square to put the equation in vertex form.
Starting with y=-x^2-4x+1, add and subtract the square of half the coefficient of x (in this case, 4) squared:
y=-(x^2+4x)+1
y=-(x^2+4x+4-4)+1
y=-(x^2+4x+4)+4+1
y=-(x+2)^2+5
Now we have the equation in vertex form y=-(x+2)^2+5, with the vertex at (-2,5). The axis of symmetry is the vertical line x=-2.