Write the equation for a parabola with a focus at (-4,3) and a directrix at y = 5.

Y=?

The equation for a parabola with a focus at (-4, 3) and a directrix at y = 5 is; y = ¹/₄(x + 4)² + 4

The standard form of the equation of a parabola is given by;

(x - h)² = 4p(y - k)

where;

We are given the coordinates of the focus of the parabola as (-4, 3)

Thus, from (h, k + p)

h = -4

k + p = 3   (eq 1)

From y = k - p,  since it has a directrix of y = 5, then;

k - p = 5   (eq 2)

→ Add equations (1) to (2) to get;

2k = 8

k = 8/2

k = 4

Put 4 for k in equation (1) to get

4 + p = 3

p = 4 - 3

p = 1

Plugging in the relevant values into the standard form of the equation of the parabola gives (x - h)² = 4p(y - k)

(x - (-4))² = 4(1)(y - 4)

⇒ (x + 4)² = 4(y - 4)

⇒ y = ¹/₄(x + 4)² + 4

The equation of the parabola is y = ¹/₄(x + 4)² + 4

Read more about equation of parabola at; link

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

they used 313 gallons of paint