Answer:
(x - 3)² - 16 = 0
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Subtract 7 from both sides
x² - 6x + 7 = 0 ← in standard form
with a = 1, b = - 6
Given a quadratic in standard form then the x- coordinate of the vertex is
= -
= -
= 3
Substitute x = 3 into the equation for y
y = 3² - 6(3) - 7 = 9 - 18 - 7 = - 16 ⇒ (h, k) = (3, - 16)
y = (x - 3)² - 16 = 0
Answer:
Part 1) The vertex is the point (-83,-9)
Part 2) The focus is the point (-82.75,-9)
Part 3) The directrix is
Step-by-step explanation:
step 1
Find the vertex
we know that
The equation of a horizontal parabola in the standard form is equal to
where
p≠ 0.
(h,k) is the vertex
(h + p, k) is the focus
x=h-p is the directrix
In this problem we have
Convert to standard form
so
This is a horizontal parabola open to the right
(h,k) is the point (-83,-9)
so
The vertex is the point (-83,-9)
step 2
we have
<em>Find the value of p</em>
<em>Find the focus</em>
(h + p, k) is the focus
substitute
(-83+1/4,-9)
The focus is the point (-82.75,-9)
step 3
Find the directrix
The directrix of a horizontal parabola is
substitute