Solve the Conversion of y = 2(x - 5)^2 - 10 to standard form.

Y = 2x^2 + ? + 40.

1 answer

To convert the given equation \( y = 2(x - 5)^2 - 10 \) to standard form, we'll start by expanding the expression.

  1. First, expand \( (x - 5)^2 \): \[ (x - 5)^2 = x^2 - 10x + 25 \]

  2. Substitute this back into the equation: \[ y = 2(x^2 - 10x + 25) - 10 \]

  3. Distribute the 2: \[ y = 2x^2 - 20x + 50 - 10 \]

  4. Combine the constant terms: \[ y = 2x^2 - 20x + 40 \]

So, the standard form of the equation is: \[ y = 2x^2 - 20x + 40 \]

In the form \( y = 2x^2 + ? + 40 \), the question mark would correspond to the coefficient of \( x \), which is \( -20 \).

Therefore, the equation in standard form is: \[ y = 2x^2 - 20x + 40 \]

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