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

Expand Squared Term: Expand the squared term (x - 2)². Reasoning: To write the quadratic function in Standard Form, we need to expand the squared term and then distribute the coefficient -5. Calculation: (x - 2)² = x² - 4x + 4Distribute Coefficient: Distribute the coefficient -5 to the expanded terms. Reasoning: Multiplying each term in the expansion by -5 will give us the quadratic in an expanded form. Calculation: -5(x² - 4x + 4) = -5x² + 20x - 20Add Constant Term: Add the constant term +3 to the result from Step 2. Reasoning: To complete the quadratic function, we add the constant term to the expression obtained after distribution. Calculation: -5x² + 20x - 20 + 3 = -5x² + 20x - 17Write Final Function: Write the final quadratic function in Standard Form. Reasoning: The Standard Form of a quadratic function is ax² + bx + c. We have all the terms from the previous steps to write the function in this form. Calculation: y = -5x² + 20x - 17

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

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Answer:

y=

Expand Squared Term: Expand the squared term $(x - 2)^2$ . $\newline$ Reasoning: To write the quadratic function in Standard Form, we need to expand the squared term and then distribute the coefficient $-5$ . $\newline$ Calculation: $(x - 2)^2 = x^2 - 4x + 4$
Distribute Coefficient: Distribute the coefficient $-5$ to the expanded terms. $\newline$ Reasoning: Multiplying each term in the expansion by $-5$ will give us the quadratic in an expanded form. $\newline$ Calculation: $-5(x^2 - 4x + 4) = -5x^2 + 20x - 20$
Add Constant Term: Add the constant term $+3$ to the result from Step $2$ . $\newline$ Reasoning: To complete the quadratic function, we add the constant term to the expression obtained after distribution. $\newline$ Calculation: $-5x^2 + 20x - 20 + 3 = -5x^2 + 20x - 17$
Write Final Function: Write the final quadratic function in Standard Form. $\newline$ Reasoning: The Standard Form of a quadratic function is $ax^2 + bx + c$ . We have all the terms from the previous steps to write the function in this form. $\newline$ Calculation: $y = -5x^2 + 20x - 17$