Re-write the quadratic function below in Standard Form y=4(x-4)^(2)-7 Answer: y=

Expand Squared Term: Expand the squared term (x-4)². Reasoning: To write the quadratic function in Standard Form, we need to expand the squared term and simplify. Calculation: (x-4)² = x² - 2*(4)*x + 4² = x² - 8x + 16Multiply by Coefficient: Multiply the expanded term by the coefficient 4. Reasoning: The quadratic function has a coefficient of 4 that needs to be distributed to each term in the expanded squared term. Calculation: 4*(x² - 8x + 16) = 4x² - 32x + 64Subtract Constant: Subtract 7 from the result of Step 2. Reasoning: The quadratic function includes a constant term -7 that needs to be combined with the result from Step 2 to complete the Standard Form. Calculation: 4x² - 32x + 64 - 7 = 4x² - 32x + 57Write Standard Form: Write the final Standard Form of the quadratic function. Reasoning: After expanding, distributing, and combining like terms, we have the quadratic function in Standard Form. Calculation: y = 4x² - 32x + 57

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Quadratic equation with complex roots

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Q. Re-write the quadratic function below in Standard Form

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y=4(x-4)^{2}-7

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Answer:

y=

Expand Squared Term: Expand the squared term $(x-4)^2$ . $\newline$ Reasoning: To write the quadratic function in Standard Form, we need to expand the squared term and simplify. $\newline$ Calculation: $(x-4)^2 = x^2 - 2\times(4)\times x + 4^2 = x^2 - 8x + 16$
Multiply by Coefficient: Multiply the expanded term by the coefficient $4$ . Reasoning: The quadratic function has a coefficient of $4$ that needs to be distributed to each term in the expanded squared term. Calculation: $4*(x^2 - 8x + 16) = 4x^2 - 32x + 64$
Subtract Constant: Subtract $7$ from the result of Step $2$ . $\newline$ Reasoning: The quadratic function includes a constant term $-7$ that needs to be combined with the result from Step $2$ to complete the Standard Form. $\newline$ Calculation: $4x^2 - 32x + 64 - 7 = 4x^2 - 32x + 57$
Write Standard Form: Write the final Standard Form of the quadratic function. $\newline$ Reasoning: After expanding, distributing, and combining like terms, we have the quadratic function in Standard Form. $\newline$ Calculation: $y = 4x^2 - 32x + 57$