To convert the given equation \( y = 2(x - 5)^2 - 10 \) to standard form, we'll start by expanding the expression.
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First, expand \( (x - 5)^2 \): \[ (x - 5)^2 = x^2 - 10x + 25 \]
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Substitute this back into the equation: \[ y = 2(x^2 - 10x + 25) - 10 \]
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Distribute the 2: \[ y = 2x^2 - 20x + 50 - 10 \]
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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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