Find the equation of a parabola with a focus at (-4, 7) and a directrix of y=1. ANSWERS ATTACHED, 15 points, due in 2 HOURS!

Solution: y - 4 = 1 / 12(x + 4)² or Option B

Step-by-step explanation:

Since the directrix is vertical, use the equation of a parabola that opens up or down -

(x - h)² = 4p(y - k)

Remember that the vertex, (h, k) is halfway between the directrix and focus. Therefore we can find the  y  coordinate of the vertex using the formula y = y coordinate of focus + directrix / 2.The  x -coordinate will be the same as the  x  coordinate of the focus.

Vertex: (- 4, 7 + 1 / 2) = (- 4,4)

Now we can find the distance from the focus to the vertex. The distance  from the vertex to the directrix is  represented by | p |. We can subtract the  y  coordinate of the vertex from the  y -coordinate of the focus to find  p.

p = 7 - 4 = 3

Substitute the known values for these variables into the given equation (x - h)² = 4p(y - k) to get our solution.

(x + 4)² = 4(3)(y - 4),

(x + 4)² = 12(y - 4)

1 / 12(x + 4)² = y - 4

y - 4 = 1 / 12(x + 4)² ~ As you can see your solution is option b.

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629

both the histogram and the stem and leaf plot will visually show how many shoppers were of various ages within each range of data.   the histogram does not give us the specific ages of these shoppers unlike the stem and leaf plot.a histogram does not give us a true range of the data because we do not know exactly how old the shoppers were. a stem and leaf plot will give exact ages, so we can determine the exact range along with all measures of center and the others measures of center.   with the histogram, we cannot find any of these.

step-by-step explanation: