Re-write the quadratic function below in Standard Form y=4(x+3)^(2)+6 Answer: y=

Expand Squared Term: Expand the squared term (x+3)². Reasoning: To write the quadratic function in standard form, we need to expand the squared term and simplify. Calculation: (x+3)² = x² + 2*(x*3) + 3² = x² + 6x + 9Multiply by Coefficient: Multiply the expanded term by the coefficient 4. Reasoning: The original function has a coefficient of 4 that needs to be distributed to each term in the expanded squared term. Calculation: 4*(x² + 6x + 9) = 4x² + 24x + 36Add Constant Term: Add the constant term 6 to the result from Step 2. Reasoning: The constant term 6 needs to be included to complete the standard form of the quadratic function. Calculation: 4x² + 24x + 36 + 6 = 4x² + 24x + 42Write Final Function: Write the final standard form of the quadratic function. Reasoning: After expanding, multiplying, and adding the constant term, we have the quadratic function in standard form. Calculation: y = 4x² + 24x + 42

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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+3)^{2}+6

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Answer:

y=

Expand Squared Term: Expand the squared term $(x+3)^2$ . $\newline$ Reasoning: To write the quadratic function in standard form, we need to expand the squared term and simplify. $\newline$ Calculation: $(x+3)^2 = x^2 + 2\cdot(x\cdot3) + 3^2 = x^2 + 6x + 9$
Multiply by Coefficient: Multiply the expanded term by the coefficient $4$ . $\newline$ Reasoning: The original function has a coefficient of $4$ that needs to be distributed to each term in the expanded squared term. $\newline$ Calculation: $4*(x^2 + 6x + 9) = 4x^2 + 24x + 36$
Add Constant Term: Add the constant term $6$ to the result from Step $2$ . $\newline$ Reasoning: The constant term $6$ needs to be included to complete the standard form of the quadratic function. $\newline$ Calculation: $4x^2 + 24x + 36 + 6 = 4x^2 + 24x + 42$
Write Final Function: Write the final standard form of the quadratic function. $\newline$ Reasoning: After expanding, multiplying, and adding the constant term, we have the quadratic function in standard form. $\newline$ Calculation: $y = 4x^2 + 24x + 42$