How would you find the intercept for the equation y^2=2-3x-2x^2? I need the steps to understand
1 answer:
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Answer:
- x-intercepts: -2, +1/2
- y-intercepts: ±√2
Step-by-step explanation:
You always find the intercepts by setting the known coordinate to its known value and solving for the value of the unknown coordinate.
An x-intercept is always found on the line y=0. Setting y=0 and solving for x, we find ...
0 = 2 -3x -2x^2
x^2 +3/2x -1 = 0 . . . . . . . . . . . . . . . . divide by -2
(x2^2 +3/2x +(3/4)^2) -1 -(3/4)^2 = 0 . . . . . complete the square
(x +3/4)^2 = 25/16 . . . . . add 25/16 and write as a square
x +3/4 = ±5/4 . . . . . . . take the square root
x = -3/4 ±5/4 = -8/4, +2/4
The x-intercepts are -2 and +1/2.
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A y-intercept is always found on the line x=0. Setting x=0 and solving for y, we find ...
y^2 = 2 -0 -0
y = ±√2
The y-intercepts are -√2 and +√2.
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A graphing calculator can give you a good idea of what the intercepts are.
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Answer:
a₁ = -5, d = 7, a₂ = 2, a₃ = 9, a₄ = 16
equation of sequence:
Step-by-step explanation:
a₁ + a₂ + a₃ = 6
a₁ + a₁ + d + a₁ + 2d = 6
3a₁ + 3d = 6
a₁ + d= 2 ⇒ a₁ = 2 - d
a₄ = 16
a₁ + 3d = 16
2 - r + 3d = 16
2d = 14
d = 7
a₁ = 2-7 = -5
a₁ = -5, d = 7 ⇒ a₂ = -5+7 = 2, a₃ = 2+7 = 9, a₄ = 9+7 = 16
equation of arithmetic sequence: