The vertex of a parabola is the point where the parabola intersects its axis of symmetry. If the coefficient of the x^2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the "U"-shape. If the coefficient of the x^2 term is negative, the vertex will be the highest point on the graph, the point at the top of the "∩"-shape. There are different ways to find the vertex of a parabola, depending on the form of the equation. Here are some methods:
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Standard Form: The standard form of a parabola is y = ax^2 + bx + c. To find the x-coordinate of the vertex, use the formula x = -b/2a. Then substitute this value of x into the equation to find the y-coordinate of the vertex. The vertex is the point (x, y) .
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Vertex Form: The vertex form of a parabola is y = a(x - h)^2 + k. The vertex is the point (h, k) .
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Completing the Square: Another way to find the vertex of a parabola in standard form is to complete the square. Rewrite the equation in the form y = a(x - h)^2 + k, where h and k are constants. The vertex is the point (h, k) .
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Geometry: The vertex of a parabola is the point where the parabola makes its sharpest turn. It is also the point of intersection of the parabola and its axis of symmetry. Every parabola has exactly one vertex.
In summary, the vertex of a parabola is the point where the parabola intersects its axis of symmetry. The x-coordinate of the vertex can be found using different formulas depending on the form of the equation, and the y-coordinate can be found by substituting the x-coordinate into the equation.
