Problem

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

Solution

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: \(y = 2\left(x^2 - \frac{3}{2}x + \left(\frac{-3}{4}\right)^2 - \left(\frac{-3}{4}\right)^2\right) - 2\)

Step 3 :Rewrite the equation in vertex form: \(y = 2\left(x - \frac{3}{4}\right)^2 - 2 + 2\left(\frac{-3}{4}\right)^2\)

Step 4 :Calculate the final equation: \(y = 2\left(x - \frac{3}{4}\right)^2 - \frac{7}{8}\)

Step 5 :\(\boxed{y = 2\left(x - \frac{3}{4}\right)^2 - \frac{7}{8}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8668/

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