How do you derive the quadratic formula? Thanks
See below.
From the form:
Start with:
Simplify left hand side:
Arrange right hand side into the square of a binomial:
Take square roots of both sides:
Add fractions:
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The quadratic formula is derived using the method of completing the square. Start with a general quadratic equation in the form ax^2 + bx + c = 0. Divide both sides by a to simplify the equation to x^2 + (b/a)x + c/a = 0. Move the constant term to the other side to isolate the terms involving x. Complete the square on the x terms by adding and subtracting (b/2a)^2 inside the parentheses. This creates a perfect square trinomial. Factor the perfect square trinomial and then solve for x to get the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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