Re-write the quadratic function below in Standard Formy, equals, 3, left bracket, x, plus, 3, right bracket, squared, minus, 3y=3(x+3) 2 −3
Question
Re-write the quadratic function below in Standard Formy, equals, 3, left bracket, x, plus, 3, right bracket, squared, minus, 3y=3(x+3) 2 −3
Solution
The given quadratic function is in vertex form, which is y=a(x-h)²+k. We need to rewrite it in standard form, which is y=ax²+bx+c.
Given function: y = 3(x+3)² - 3
First, expand the squared term:
y = 3(x² + 6x + 9) - 3
Then, distribute the 3:
y = 3x² + 18x + 27 - 3
Finally, simplify the constant terms:
y = 3x² + 18x + 24
So, the quadratic function in standard form is y = 3x² + 18x + 24.
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