42+66 What's the answers
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Answer:
Part 1) The directrix of the parabola is y=-4.25
Part 2) The focus of the parabola is F(1,-3.75)
Step-by-step explanation:
we have
This is a vertical parabola open upward
we know that
If a parabola has a vertical axis, the standard form of the equation of the parabola is
where
p≠ 0
The vertex of this parabola is at (h, k).
The focus is at (h, k + p).
The directrix is the line y = k - p.
The axis is the line x = h.
step 1
Convert the equation of the parabola in standard form
so
----> equation in standard form
The vertex is the point (1,-4)
4p=1 ------> p=1/4
step 2
Find the directrix of the parabola
The directrix is the line y = k - p
we have
k=-4
p=1/4
substitute the values
y = k - p
y=-4-(1/4)=-17/4
y=-4.25
step 3
Find the focus of the parabola
we know that
The focus is at (h, k + p).
we have
h=1
k=-4
p=1/4
substitute
F(1,-4+1/4)
F(1,-3.75)
Step-by-step explanation: To solve for x in this inequality,
your goal is the same as it would be if you were solving an
equation, to get x by itself on one side.
Since 5 is being subtracted from x, add 5 to both sides of the inequality.
On the left, the -5and +5 cancel out and on the right, -2 + 5 is 3.
So we have x ≥ 3.
When graphing, start with a closed dot at +3 because x is
not just greater than +3, it's equal to it as well.
Then draw an arrow to the right, like I have done below.
