Question

How would you find the intercept for the equation y^2=2-3x-2x^2? I need the steps to understand

Answer 1

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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.