give me an example of parabula equations
Answer (1)
Answer:Here are a few examples of parabola equations:Standard Form: \(y = x^2\)Vertex Form: \(y = a(x-h)^2 + k\)Example: \(y = 2(x-3)^2 + 4\) (Here, the vertex is at (3, 4))General Form: \(Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0\) (where \(B^2 - 4AC = 0\))Example: \(y^2 - 4x + 2y - 3 = 0\)Key Concepts/Tips:The standard form \(y = x^2\) represents a basic parabola opening upwards with its vertex at the origin (0, 0).The vertex form \(y = a(x-h)^2 + k\) makes it easy to identify the vertex of the parabola, which is at the point (h, k). The 'a' value determines whether the parabola opens upwards (if a > 0) or downwards (if a < 0), and how wide or narrow it is.The general form is less intuitive but can be converted to other forms through algebraic manipulation (completing the square).Step-by-step explanation:
