Question

A. Sabiendo que el vértice de una parábola presenta las coordenadas V(2,-3) y su foco f(2,-2), realiza la gráfica y encuentra los siguientes valores:

Distancia p=
Lado recto LR =
¿Hacia dónde abre la parábolar R:
Ecuación ordinaria:

Answer 1

To find the values requested, you can use the equations that describe the properties of a parabola. The distance p is -1, the length of the latus rectum (LR) is 4, the parabola opens upwards, and the equation in standard form is y = ax^2 - 4ax + (4a - 3).

Step-by-step explanation:

To find the values requested, we can use the equations that describe the properties of a parabola. The equation of a parabola in vertex form is given by y = a(x-h)^2 + k, where (h, k) are the coordinates of the vertex. In this case, the vertex is V(2, -3), so the equation becomes y = a(x-2)^2 - 3. The focus of the parabola is given by the coordinates (h+p, k), where p is the distance from the vertex to the focus. In this case, the focus is f(2, -2), which means p = -3 - (-2) = -1. Therefore, the distance p is -1.

The length of the latus rectum (LR) of a parabola is given by the equation 4a, where a is the coefficient of x^2 in the equation of the parabola. In this case, the equation is y = a(x-2)^2 - 3, so LR = 4a = 4. Therefore, the length of the latus rectum is 4.

Since the coefficient of x^2 is positive in the equation y = a(x-2)^2 - 3, the parabola opens upwards. The equation in standard form (or ordinary form) is y = ax^2 + bx + c. Expanding the vertex form equation, we get y = ax^2 - 4ax + 4a - 3. Comparing this with the standard form equation, we can see that b = -4a and c = 4a - 3. Therefore, the equation in standard form is y = ax^2 - 4ax + (4a - 3).