Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?

f(x) = (x - 2)² + 2

Step-by-step explanation:

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

Using the distance formula

= | y + 2 | ← square both sides

(x - 2)² + (y - 6)² = (y + 2)² ← subtract (y + 2)² from both sides

(x - 2)² + (y - 6)² - (y + 2)² = 0 ← subtract (x - 2)² from both sides

(y - 6)² - (y + 2)² = - (x - 2)² ← expand left side using FOIL and simplify

y² - 12y + 36 - y² - 4y - 4 = - (x - 2)²

- 16y + 32 = - (x - 2)² ← subtract 32 from both sides

- 16y = - (x - 2)² - 32 ← divide all terms by - 16

y = (x - 2)² + 2

168

step-by-step explanation:

first off, we know that he drove 3.5 hours at a rate of 48 mph.

knowing that, we want to see how many miles he drove all-together.

in this case, we can just multiply 48 by 3.5.

48 * 3.5 = 168

step-by-step explanation:

a child is 12 years old, and his father is 32 years older. in how many years will the age of the father be 2 times the age of the child?

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this needs to be the answer format, or else your answer is incomplete.

if the number of years is x, then the equation is

in __ years