Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = − one half . (2 points) f(x) = −(x + 2)2 − three fourths f(x) = (x + 2)2 + three fourths f(x) = −(x − 2)2 + three fourths f(x) = −(x − 2)2 − three fourths

Step-by-step explanation:

The parabola must have all the points to be equally distant from the point of focus and the directrix, where directrix a horizontal line and the focus being a point given.

To derive an equation for the parabola, we will use the formula of distance. Now we have a random point on the parabola (x,y) and the point (x,y) will be equidistant from the focus and the directrix. So using the distance formula, we will get:

The square root of y-(-1/2) from the directrix, and the righthand side of the equal sign is derived from the focus point. Now simplify it to get:

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im alright what do you need

step-by-step explanation:

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40