Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. put the equation in standard form.

f(x) = one fourthx2 − x + 4
f(x) = −one fourthx2 − x + 4
f(x) = one fourthx2 − x + 5
f(x) = −one fourthx2 − x + 5

B

Step-by-step explanation:

From any point (x, y) on the parabola the focus and directrix are equidistant.

Using the distance formula

= | y - 6 |

Squaring both sides

(x + 2)² + (y - 4)² = (y - 6)² ←  distributing

x² + 4x + 4 + y² - 8y + 16 = y² - 12y + 36 ( subtract y² - 12y + 36 from both sides )

x² + 4x + 4 + 4y - 20 = 0 ( subtract x² + 4x + 4 from both sides )

4y - 20 = - x² - 4x - 4 ( add 20 to both sides )

4y = - x² - 4x + 16 ( divide through by 4 )

y = - x² - x + 4, that is

f(x) = - x² - x + 4 → B

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3