The minimum value at -1 ⇒ D
Step-by-step explanation:
The completing square form of ax² + bx + c is a(x - h)² + k, where
- k is the value of of the expression when x = h
- k is minimum if a > 0 and maximum if a < 0
∵ The expression is x² + 4x + 3
∴ a = 1 , b = 4 , c = 3
- Use the rule above to find h
∵
∴ h = -2
- To find k substitute x by the value of h
∵ k = (-2)² + 4(-2) + 3 = 4 - 8 + 3
∴ k = -1
- Substitute h and k in the form of the completing square
∵ a(x - h)² + k = 1(x - -2)² + (-1)
∴ a(x - h)² + k = (x + 2)² - 1
∴ x² + 4x + 3 = (x + 2)² - 1
∵ The completing square is (x + 2)² - 1
∵ a = 1 ⇒ greater than zero
∴ The value is minimum
- The minimum value is the value of k
∵ k = -1
∴ The minimum value of the function is -1
The minimum value at -1
Learn more:
You can learn more about the quadratic function in brainly.com/question/9390381
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