To find the vertex of a parabola given its equation in standard form (y = ax² + bx + c), follow these steps:
-
Identify a, b, and c: In the standard form equation y = ax² + bx + c, identify the coefficients a, b, and c.
-
Calculate the x-coordinate of the vertex (h): Use the formula h = -b / 2a. This value represents the x-coordinate of the vertex.
-
Calculate the y-coordinate of the vertex (k): Substitute the x-coordinate (h) you just calculated back into the original equation y = ax² + bx + c. Solve for y. This value represents the y-coordinate of the vertex.
-
Write the vertex: The vertex is the point (h, k), where h is the x-coordinate and k is the y-coordinate calculated above.
Example:
Let's say you have the equation y = 2x² + 8x - 3.
-
Identify a, b, and c: a = 2, b = 8, c = -3
-
Calculate the x-coordinate (h): h = -b / 2a = -8 / (2 * 2) = -8 / 4 = -2
-
Calculate the y-coordinate (k): Substitute x = -2 into the equation:
y = 2(-2)² + 8(-2) - 3
y = 2(4) - 16 - 3
y = 8 - 16 - 3
y = -11 -
Write the vertex: The vertex is (-2, -11).
In summary, finding the vertex from the standard form of a quadratic equation involves using the formula -b/2a to find the x-coordinate, substituting that value back into the equation to find the y-coordinate, and expressing the vertex as a coordinate point.
