Answer:
Step-by-step explanation:
The general form of a quadratic polynomial is given by:
(1)
You have the following polynomial:
(2)
In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:
(3)
By comparing the equation (1) with the equation (2) you obtain:
a = 3
b = -10
c = 8
Then, you replace these values in the equation (3):
Then, the factorization of the polynomial is:
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)