Answer:
Step-by-step explanation:
The first parabola has vertex (-1, 0) and y-intercept (0, 1).
We plug these values into the given vertex form equation of a parabola:
y - k = a(x - h)^2 becomes
y - 0 = a(x + 1)^2
Next, we subst. the coordinates of the y-intercept (0, 1) into the above, obtaining:
1 = a(0 + 1)^2, and from this we know that a = 1. Thus, the equation of the first parabola is
y = (x + 1)^2
Second parabola: We follow essentially the same approach. Identify the vertex and the two horizontal intercepts. They are:
vertex: (1, 4)
x-intercepts: (-1, 0) and (3, 0)
Subbing these values into y - k = a(x - h)^2, we obtain:
0 - 4 = a(3 - 1)^2, or
-4 = a(2)². This yields a = -1.
Then the desired equation of the parabola is
y - 4 = -(x - 1)^2
A. 8.6 × 10¹²
b. 8.6 × 10¹¹
c. 8.6 × 10⁻¹³
d. 8.6 × 10⁻¹³
Answer:
16 square units
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
Here, it is convenient to choose the base as the vertical segment between y=-5 and y=3. Its length is 3 -(-5) = 8 units.
The height of the triangle is the difference in x-coordinates between that segment and the opposite vertex: 6 -2 = 4.
Then the area is ...
A = 1/2(8)(4) = 16 . . . square units
Answer:
AB=24
Step-by-step explanation:
4y=y+18
4y-y=18
3y=18
Y=6
4×6=24
AB=24