Problem

Find the vertex form of the parabola given by the equation \(y = 2x^2 - 12x + 20\).

Answer

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Answer

Simplify to find the vertex form: \(y = 2(x - 3)^2 - 18 + 20 = 2(x - 3)^2 + 2\).

Steps

Step 1 ：Rewrite the equation in the form \(y = a(x-h)^2 + k\).

Step 2 ：Factor out the leading coefficient from the first two terms: \(y = 2(x^2 - 6x) + 20\).

Step 3 ：Complete the square on the \(x\) terms: \(y = 2[(x - 3)^2 - 9] + 20\).

Step 4 ：Simplify to find the vertex form: \(y = 2(x - 3)^2 - 18 + 20 = 2(x - 3)^2 + 2\).

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