Find the roots of y=x^2, axis of symmetry and vertex.
I got
roots: (0,0)
axis of symmetry: minimum point x=0
vertex: (0,0)
axis is the line x=0
so im right?
with the exception of calling the vertex the axis of symmetry, yes. The axis always passes through the vertex, but it is not the vertex; the vertex is just a point. The axis has no minimum point; it is a line.
To find the roots of the equation y = x^2, we need to set y equal to zero and solve for x. Since the equation is a quadratic equation in the form of y = ax^2 + bx + c, where a = 1, b = 0, and c = 0, we can substitute these values into the equation.
0 = x^2
To solve for x, we can take the square root of both sides of the equation:
√0 = √x^2
0 = x
Therefore, the root of the equation y = x^2 is x = 0. So, you are correct that the roots are (0, 0).
The axis of symmetry of a quadratic equation in the form of y = ax^2 + bx + c is given by the equation x = -b/(2a). In this case, since b = 0, the axis of symmetry is x = -0/(2*1), which simplifies to x = 0. So, you are correct that the axis of symmetry is x = 0.
The vertex of a quadratic equation is the minimum or maximum point on the parabolic curve. For a quadratic equation in the form of y = ax^2 + bx + c, the x-coordinate of the vertex is given by -b/(2a), which we found earlier to be x = 0. To find the y-coordinate of the vertex, we substitute the x-coordinate into the equation. In this case, we substitute x = 0 into the equation y = x^2:
y = 0^2
y = 0
Therefore, the vertex of the equation y = x^2 is (0, 0), which again matches your answer.
In summary:
- The roots of the equation y = x^2 are (0, 0).
- The axis of symmetry is x = 0.
- The vertex is (0, 0).