Write the equation for a parabola with a focus at (1,-4)(1,−4)left parenthesis, 1, comma, minus, 4, right parenthesis and a directrix at x=2x=2x, equals, 2.

x = 3/2 - ((y + 4)²)/2

Step-by-step explanation:

The coordinates of the focus of the parabola = (1, -4)

The directrix of the parabola is the line, x = 2 (parallel to the y-axis)

The general form of a parabola having a directrix parallel to the y-axis is presented as follows;

(y - k)² = 4·p·(x - h)

The coordinates of the focus = (h + p, k)

The line representing the directrix is x = h - p

Therefore, by comparison, we have;

(1, -4) = (h + p, k)

k = -4

h + p = 1

∴ p = 1 - h

From the directrix, we have;

2 = h - p

∴ 2 = h - (1 - h) = 2·h - 1

2·h = 2 + 1

h = 3/2

p = 1 - h

∴ p = 1 - 3/2 = -1/2

p = -1/2

By substitution of the values of k, p, and h, in the general equation of the parabola, (y - k)² = 4·p·(x - h), we get;

(y - k)² = 4·p·(x - h) = (y - (-4))² = 4·(-1/2)·(x - (3/2)) = (y + 4)² = -2·(x - 3/2)

The equation of the parabola in vertex form is therefore;

x = (-1/2)·(y + 4)² + 3/2 = 3/2 - (y + 4)²/2

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step-by-step explanation:

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05