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Question

write the quadratic function given in vertex form as y= 3 (x - 2)^2+5 in standard form write it in form y=ax^2 + bx + c .

Answer 1

The function in vertex form y = 3(x - 2)² + 5

Apply the formula (a - b)² = a² + b² - 2ab

In this case a = x, b = 2

y = 3(x² + 4 - 4x) + 5

y = 3x² + 12 - 12x + 5

y = 3x² - 12x + 17

Now it is in the form y = ax² + bx + c

a = 3, b = - 12, c = 17.