how do I solve the parabola 8y=(x-1)^2-4

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Step 1:  Write the equation in standard form.

8y = (x - 1)^2 - 4

8y = (x - 1)(x - 1) - 4

8y = x^2 + (-2x) + 1 + (-4)

8y = x^2 + (-2x) + (-3)

y = (x^2 + (-2x) + (-3)) / 8

y = 0.125x^2 + (-0.25x) + (-0.375)

Step 2:  Identify a, b, and c.

a = 0.125

b = -0.25

c = -0.375

Step 3:  Use the quadratic equation.

x = (-b `+-` sqrt(b^2 - 4ac)) / 2a

b^2 = (-0.25)^2 = 0.0625

4ac = 4 * 0.125 * -0.375 = - 0.1875

b^2 - 4ac = 0.0625 - (-0.1875) = 0.25

sqrt(0.25) = 0.5

-b `+-` sqrt(b^2 - 4ac) = 0.25 `+-` 0.5

2a = 2 * 0.125 = 0.25

(0.25 `+-` 0.5) / 0.25

(0.25 + 0.5) / 0.25 = 0.75 / 0.25 = 3

(0.25 - 0.5) / 0.25 = -0.25 / 0.25 = -1

Solutions:  x = 3 and x = -1

The solutions to a parabola can be checked by graphing.

The parabola intersects the x-axis at the two solutions:  -1 and 3.

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