to practice writing the equations of vertical parabolas, write the equations of these parabolas in vertex form:

focus at (-5, -3), and directrix y = -6
focus at (10, -4), and directrix y = 6.

1. y = (1/6)(x +5)^2 -4.5

2. y = (-1/20)(x -10)^2 +1

Step-by-step explanation:

For focus (p, q) and directrix y=r, the equation is ...

y = 1/(2(q-r))·(x -p)^2 +(q+r)/2

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1. For (p, q) = (-5, -3) and r = -6, the equation is ...

y = 1/(2(-3-(-6))(x -(-5))^2 +(-3-6)/2

y = 1/6(x +5)^2 -4.5

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2. for (p, q) = (10, -4) and r = 6, the equation is ...

y = 1/(2(-4-6))(x -10)^2 +(-4+6)/2

y = (-1/20)(x -10)^2 +1

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80