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csands
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The vertex of a parabola is the point where the parabola changes direction from increasing to decreasing or vice versa. It is the highest or lowest point on the parabola depending on whether it opens upwards or downwards.
To find the vertex of a parabola, you can use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in the form ax^2 + bx + c. This value of x represents the x-coordinate of the vertex. To find the y-coordinate, you can substitute this value of x into the original equation and solve for y.
The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two symmetrical halves. The equation of the axis of symmetry is x = -b/2a, which is the same as the x-coordinate of the vertex. Therefore, the vertex and the axis of symmetry are the same point on the coordinate plane.
Yes, a parabola can have a vertex at the origin. This occurs when the quadratic equation is in the form y = ax^2, where a is the coefficient and the y-intercept is 0. In this case, the vertex is at (0,0) and the axis of symmetry is the y-axis.
There are two main ways to find the vertex of a parabola. The first is by using the formula x = -b/2a, as mentioned earlier. The second method is by completing the square, where you manipulate the quadratic equation into the form a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex. Both methods will give you the same result.