Re-write the quadratic function below in Standard Formy, equals, 4, left parenthesis, x, plus, 2, right parenthesis, squared, minus, 4y=4(x+2) 2 −4
Question
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 = 4(x + 2)² - 4
First, expand the squared term:
y = 4(x² + 4x + 4) - 4
Then distribute the 4:
y = 4x² + 16x + 16 - 4
Finally, simplify the constants:
y = 4x² + 16x + 12
So, the standard form of the given quadratic function is y = 4x² + 16x + 12.
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