vertex of a parabola
The lowest point on a parabola that opens up or the highest point on a parabola that opens down
The vertex of a parabola is the point where the parabola changes direction. It is the highest or lowest point on the curve, depending on whether the parabola opens upwards or downwards. The vertex of a parabola can be found using the formula (-b/2a, f(-b/2a)), where a and b are coefficients of the quadratic equation that represents the parabola in standard form, and f(-b/2a) is the y-coordinate of the vertex.
Alternatively, the vertex can also be found by completing the square of the quadratic equation. To do this, first rewrite the quadratic equation in standard form (y = ax^2 + bx + c), where a, b, and c are constants. Then, divide the coefficient of x by 2 and square the result, i.e., (b/2)^2. Add this value to both sides of the equation, i.e., add (b/2)^2 to both sides of y = ax^2 + bx + c. This will result in a perfect square trinomial on the right-hand side of the equation, which can be factored into (ax + b/2)^2. This expression can be rewritten as y – k = a(x – h)^2, where (h,k) is the vertex of the parabola.
In summary, the vertex of a parabola is a crucial feature of the curve, as it provides information about the maximum or minimum point on the curve, depending on its orientation. It can be found using either the formula (-b/2a, f(-b/2a)) or by completing the square.
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