The vertex form of the equation if a parabola is y = 3(x - 4)^2 - 22. What is the standard form of the equation?

A.) Y = 9x^2 - 26

B.) Y = 3x^2 - 18

C.) Y = 3x^2 - 24x + 26

D.) Y = 3x^2 - 24x + 4

The answer is (C) Y = 3x² - 24x + 18

Step-by-step explanation:

Y = 3(x-4)² - 22

First step is to simplify (x-4)²

⇒ Y= 3(x-4)(x-4)-22

⇒ Y= 3(x²- 4x - 4x + 16) - 22 = 3(x² - 8x + 16) - 22

Next step is to open the parenthesis

⇒ Y = 3x² - 24x + 48 - 22

The final step is to collect like terms and simplify the equation

⇒ Y = 3x² - 24x + 26

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step-by-step explanation: