To rewrite the given quadratic function in Standard Form, expand and simplify the expression. The standard form of a quadratic function is:

$y = ax^2 + bx + c$

Given:

$y = 2(x - 5)^2 - 3$

Step 1: Expand $(x - 5)^2$

$(x - 5)^2 = x^2 - 10x + 25$

Step 2: Distribute the 2 to each term

$2(x^2 - 10x + 25) = 2x^2 - 20x + 50$

Step 3: Subtract 3 from the result

$y = 2x^2 - 20x + 50 - 3$

$y = 2x^2 - 20x + 47$

Final Answer:

$y = 2x^2 - 20x + 47$

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Related Questions:

1. How do you convert any quadratic function from vertex form to standard form?
2. What is the process for completing the square to convert standard form to vertex form?
3. What is the vertex of this quadratic equation, and how do we find it?
4. How do you determine if the quadratic opens upwards or downwards?
5. What is the role of the constant term in the standard form?

Tip:

The coefficient of $x^2$ in the standard form determines the parabola's "width" and direction (narrower for larger values, wider for smaller values).