Re-write the quadratic function below in Standard Form y=3(x+5)^(2)-1 Answer: y=

Expand Squared Term: Expand the squared term (x+5)². Reasoning: To write the quadratic function in standard form, we need to expand the squared term and simplify. Calculation: (x+5)² = x² + 2*(5)*x + 5² = x² + 10x + 25Multiply by Coefficient: Multiply the expanded term by the coefficient 3. Reasoning: The quadratic function has a coefficient of 3 that needs to be distributed to each term in the expansion. Calculation: 3*(x² + 10x + 25) = 3x² + 3*10x + 3*25 = 3x² + 30x + 75Subtract from Result: Subtract 1 from the result. Reasoning: The quadratic function has a constant term -1 that needs to be included in the standard form. Calculation: 3x² + 30x + 75 - 1 = 3x² + 30x + 74Write Final Standard Form: Write the final standard form of the quadratic function. Reasoning: After expanding, multiplying, and subtracting, we have the standard form of the quadratic function. Calculation: y = 3x² + 30x + 74

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Algebra 2

Quadratic equation with complex roots

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

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y=3(x+5)^{2}-1

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Answer:

y=

Expand Squared Term: Expand the squared term $(x+5)^2$ . $\newline$ Reasoning: To write the quadratic function in standard form, we need to expand the squared term and simplify. $\newline$ Calculation: $(x+5)^2 = x^2 + 2\cdot(5)\cdot x + 5^2 = x^2 + 10x + 25$
Multiply by Coefficient: Multiply the expanded term by the coefficient $3$ . $\newline$ Reasoning: The quadratic function has a coefficient of $3$ that needs to be distributed to each term in the expansion. $\newline$ Calculation: $3*(x^2 + 10x + 25) = 3x^2 + 3*10x + 3*25 = 3x^2 + 30x + 75$
Subtract from Result: Subtract $1$ from the result. $\newline$ Reasoning: The quadratic function has a constant term $-1$ that needs to be included in the standard form. $\newline$ Calculation: $3x^2 + 30x + 75 - 1 = 3x^2 + 30x + 74$
Write Final Standard Form: Write the final standard form of the quadratic function. $\newline$ Reasoning: After expanding, multiplying, and subtracting, we have the standard form of the quadratic function. $\newline$ Calculation: $y = 3x^2 + 30x + 74$