The minimum value of the function is -5.
Here's the function Yuna created after completing the square, along with the minimum value:
Function in vertex form:
f(x) = (x + 3)² - 5
Minimum value:-5
Step-by-step explanation:
Completing the square:
Take half of the coefficient of x (which is 6), square it (9), and add and subtract it within the function:
f(x) = x² + 6x + 4 + 9 - 9
Rearrange terms to group the perfect square:
f(x) = (x² + 6x + 9) + 4 - 9
Express the perfect square as a squared term:
f(x) = (x + 3)² - 5
Finding the minimum value:
The function is now in vertex form: f(x) = a(x - h)² + k, where (h, k) is the vertex.
In this case, the vertex is (-3, -5).
Since the coefficient of the squared term (a) is positive (1), the parabola opens upward, meaning the vertex represents the minimum point.
Therefore, the minimum value of the function is -5.