Answer:
y = 1/6 x^2 + 8/3 x + 49/6
Step-by-step explanation:
This is a parabola which opens upwards.
The distance of a point (x, y) from the focus is
√[(x - -8)^2 + (y - -1)^2] and
the distance of the point from the line y = -4
= y - -4
These distances are equal for a parabola so:
√[(x - -8)^2 + (y - -1)^2] = y + 4
Squaring both sides:
(x + 8)^2 + (y + 1)^2 = (y + 4)^2
x^2 + 16x + 64 + y^2 + 2y + 1 = y^2 + 8y + 16
x^2 + 16x + 64 + 1 - 16 = 8y - 2y
6y = x^2 + 16x + 49
y = 1/6 x^2 + 8/3 x + 49/6 is the equation of the parabola.
Answer:
You could use a graphing calculator to see the lowest point in the graph OR you could put that equation into it's completed squared form, which is (x-4)^2 -4. The opposite of -4 in the parentheses is positive 4, and the leftover -4 is the y value. So that also becomes (4,-4)
Answer:
x = 5
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles in the triangle and equate to 180, that is
10x - 4 + 8x + 3 + 91 = 180
18x + 90 = 180 ( subtract 90 from both sides )
18x = 90 ( divide both sides by 18 )
x = 5
Answer: y=0,5x²-x-1,5.
Step-by-step explanation:
We summarize (1) and (3):
Substitute b=-1 into (2):
From (5) subtract (4):
Substitute a=0,5 into (4):
Hense:
y=0,5x²-x-1,5.
