convert 2 x^{2}-3 x-2 to vertex form

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Accepted Answer

Step:1 ：Factor out the coefficient of the x^2 term: (y = 2(x^2 - frac{3}{2}x) - 2)Step:2 ：Complete the square by adding and subtracting the square of half of the coefficient of the x term: (y = 2left(x^2 - frac{3}{2}x + left(frac{-3}{4}right)^2 - left(frac{-3}{4}right)^2right) - 2)Step:3 ：Rewrite the equation in vertex form: (y = 2left(x - frac{3}{4}right)^2 - 2 + 2left(frac{-3}{4}right)^2)Step:4 ：Calculate the final equation: (y = 2left(x - frac{3}{4}right)^2 - frac{7}{8})Step:5 ：(boxed{y = 2left(x - frac{3}{4}right)^2 - frac{7}{8}})

Answer

Step: 1 ：Factor out the coefficient of the x^2 term: (y = 2(x^2 - frac{3}{2}x) - 2)Step: 2 ：Complete the square by adding and subtracting the square of half of the coefficient of the x term: (y = 2left(x^2 - frac{3}{2}x + left(frac{-3}{4}right)^2 - left(frac{-3}{4}right)^2right) - 2)Step: 3 ：Rewrite the equation in vertex form: (y = 2left(x - frac{3}{4}right)^2 - 2 + 2left(frac{-3}{4}right)^2)Step: 4 ：Calculate the final equation: (y = 2left(x - frac{3}{4}right)^2 - frac{7}{8})Step: 5 ：(boxed{y = 2left(x - frac{3}{4}right)^2 - frac{7}{8}})

convert $2 x^{2}-3 x-2$ to vertex form

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