The standard form equation of a parabola is y = ax^2 + bx + c, where a, b, and c are constants. This form is useful for graphing and identifying key features of the parabola.
The vertex of a parabola is located at the point (h, k), where h is the x-coordinate and k is the y-coordinate. To find the vertex, use the formula h = -b/2a and plug in the values of a and b from the standard form equation. Then, substitute h into the equation to find the corresponding y-coordinate.
To verify if a given equation is a parabola, check if it follows the standard form y = ax^2 + bx + c. If the equation does not follow this form, it is not a parabola. Additionally, you can graph the equation and see if it forms a U-shaped curve, which is characteristic of a parabola.
The origin, (0,0), is the point where the x-axis and y-axis intersect. In a parabola equation, the origin represents the point where the parabola is symmetrical and the y-value is equal to 0. This point is also the minimum or maximum point of the parabola, depending on the direction of the opening.
To verify the equation y = 1/9x^2, plug in the x-coordinate of the given point into the equation and solve for y. If the resulting y-value matches the y-coordinate of the given point, then the point lies on the parabola and can be used to verify the equation.