How to Solve Quadratic Equations in Vertex Form
- 1). Set y equal to zero in the equation. If your equation is y = 2(x + 3)^2 - 8, for example, it becomes 0 = 2(x + 3)^2 - 8 when y = 0.
- 2). Subtract k from both sides of the equation. For 0 = 2(x + 3)^2 - 8, k = -8, so subtract -8 from both sides. Remember subtracting a negative is the same as adding a positive, so 0 - (-8) = 2(x + 3)^2 - 8 - (-8) becomes 8 = 2(x + 3)^2.
If the number on the left side of the equation is negative, the equation does not have any solutions. Stop here and record the result as "no solution." - 3). Divide both sides of the equation by a to isolate the term containing the variable. For 8 = 2(x + 3)^2, a = 2, so divide both sides by 2 to get 4 = (x + 3)^2.
- 4). Take the square root of both sides of the equation. Remember that the square root of a positive number can be positive or negative, so for 4 = (x + 3)^2, you get x + 3 = 2 or -2.
- 5). Subtract the constant on the left side of the equation from both sides to find the values of x. For x + 3 = 2 or -2, subtracting 3 from both sides gives x + 3 - 3 = 2 - 3 or -2 - 3, so x = -1 and x = -5. Record the solution with the lower value first; in this case, the solution is x = -5, -1.
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