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Axis of symmetry formula for a parabola is, x = -b/2a. Let us derive the equation of the axis of symmetry. The quadratic equation of a parabola is, y = ax 2 + bx + c (up/down parabola). The constant term 'c' does not affect the parabola.Therefore, let us consider, y = ax 2 + bx.
One formula works when the parabola's equation is in vertex form and the other works when the parabola's equation is in standard form . Standard Form If your equation is in the standard form $$ y = ax^2 + bx + c $$ , then the formula for the axis of symmetry is: $ \red{ \boxed{ x = \frac {-b}{ 2a} }} $
Aug 3, 2023 · The vertex form of a quadratic equation is y = a (x – h) 2 + k, Equation of axis of symmetry is, x = h, here (h, k) = vertex of the parabola. We obtain the vertex of the function (x, y) by substituting the value of x in the standard form of the equation and get the value of y. Let us solve some examples involving the above formulas and concepts.
Oct 8, 2024 · This is the equation of the axis of symmetry for parabolas in the standard form y = ax 2 + bx + c. Similarly, if the parabola opens horizontally (i.e., left/right), we can get the equation for the axis of symmetry by finding the midpoint of the y-intercepts. Finding the Axis of Symmetry of the Parabola y = 2x2 + 8x + 5.
Since the parabola is symmetrical around its vertex, the axis of symmetry is a vertical line passing through the vertex. Therefore, the axis of symmetry is x = 1. Example 3. Write the equation for the axis of symmetry. y = x 2 + 8 x + 11. Solution: The vertex of the parabola is at (− 4, − 5).
Sep 23, 2022 · The axis of symmetry of the parabola whose vertex is \((h, k)\) and opens up/down is \(x = h\). The axis of symmetry of the parabola whose vertex is \((h, k)\) and opens to the left/right is \(y = k\). Axis of symmetry formula. The equation of the axis of symmetry can be shown when a parabola is in two forms: Standard form:
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Jan 3, 2024 · To derive the Axis of Symmetry for a parabola, we start with the quadratic function y = ax² + bx + c. This is set to zero and solved for x, yielding the formula x = -b/2a. This value of x represents the x-coordinate of the vertex of the parabola, which is the Axis of Symmetry. It’s where the parabola reaches its peak (or valley) and shows ...
