## THIS USER ASKED ๐

**Find the vertex, focus, directrix, and focal width of the parabola.**

**x2 = 28y
Vertex: (0, 0); Focus: (0, -7); Directrix: x = -7; Focal width: 112
Vertex: (0, 0); Focus: (7, 0); Directrix: x = 7; Focal width: 7
Vertex: (0, 0); Focus: (0, 7); Directrix: y = -7; Focal width: 28
Vertex: (0, 0); Focus: (7, 0); Directrix: y = 7; Focal width: 112**

## THIS IS THE BEST ANSWER ๐

1) We have the equation , so y = x ^ 2/20. The standard equation of such an equation is y =. Hence, p = 5 in this case. The focus is at (0,5) and the guideline is y = -5 (a tip is that the Directrix is โโalways “opposite” a parabolic focal point; if the guideline is at x = -7 for example, whether the focus is at (7,0)).

2) Similarly, we have the equation . So p = 1/12. In this case, the parabola is opened along the x-axis and the focus is at (1/12, 0). Also, the guideline is at x = -1 / 12. So B. is the correct answer

3) We are told that the parabola has an ap of 9.. Also, the focus is along the y-axis, so the parabola is opening along the y-axis. Eventually, the focus is on the positive half, so the parabola opens upwards. The equation for this case is y =.

4) Same as above. The directrix is โโredundant, we only need the p-value. The same comments apply under the parable and if p = 8 is substituted in the formula: we get y =.

5) This is a little different, though we don’t need the guideline again. The focus is on the x-axis, so the parabola opens in this direction. The focus is on the positive part of the axis, so the parabola on the right opens. We are also given p = 7. Hence, what we need is the equation of the form. Substituting p = 7, we find .

6) The form y = -ax ^ 2 is a prabola equation with a vertex at (0,0). The minus sign is required since the parabola is down. Since we are given an anothe point, we can. We have to take y = -74 and x = 14 feet (since 28 is left to right, we have to take half). . So a = 0.378. So y = -0.378 * is the correct expressions

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