Question

What is the equation of the parabola?

a) y = -1/20(x-3)²
b) y = -1/20(x+3)²
c) y = 1/20(x-3)²
d) y = 1/20(x+3)²

Answer 1

The equation of the parabola is y = -1/20(x-3)², option a). The vertex form of a parabola is y = a(x-h)² + k, where (h, k) represents the vertex. The parabola opens downwards and is symmetric about the line x = 3.

The correct answer is A.

Step-by-step explanation:

The equation of the parabola is given by y = -1/20(x-3)², option a). This equation is in the vertex form, y = a(x-h)² + k, where (h, k) represents the vertex of the parabola. In this case, the vertex is (3, 0), which means the parabola opens downwards and is symmetric about the vertical line x = 3. The coefficient -1/20 determines the steepness of the curve.

Answer 2

The question asks for the equation of a parabola, which is typically in the form y = ax^2 + bx + c, or the vertex form y = a(x - h)^2 + k. Without further information or a graph, it's not possible to definitively choose the correct equation from the given options.

Step-by-step explanation:

The equation of a parabola is typically represented in the form y = ax^2 + bx + c, where a, b, and c are constants. The general vertex form of a parabola's equation is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. If the coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, the parabola opens downwards.

To find the correct equation of the parabola from the given options, we must identify the vertex and the direction in which the parabola opens. Given the options:

• y = -1/20(x - 3)^2
• y = -1/20(x + 3)^2
• y = 1/20(x - 3)^2
• y = 1/20(x + 3)^2

Since all the options have the coefficient 'a' as 1/20 or -1/20, the parabola is either opening upwards (positive 'a') or downwards (negative 'a'). Without additional context or graph, we cannot determine the correct equation among these options. However, if provided with a graph or additional points the parabola passes through, we could then identify the correct option.