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PLEASE HELP!! Identify the minium value of the function

y=x^2+6x+9


A. 0

B. -3

C. 1

D. 9

PLEASE HELP!! Identify the minium value of the function y=x^2+6x+9 A. 0 B. -3 C. 1 D-example-1

1 Answer

6 votes
Because this is a positive parabola, it opens upwards, like a cup, and the vertex dictates what the minimum value of the function is. In order to determine the vertex, I recommend completing the square. Do that by first setting the function equal to 0 and then moving the 9 to the other side by subtraction. So far:
x^2+6x=-9. Now, to complete the square, take half the linear term, square it, and add that number to both sides. Our linear term is 6. Half of 6 is 3 and 3 squared is 9. So add 9 to both sides.
x^2+6x+9=-9+9. The right side reduces to 0, and the left side simplifies to the perfect square binomial we created while completing this process.
(x+3)^2=0. Move the 0 back over and the vertex is clear now. It is (-3, 0). Therefore, 0 is the minimum point on your graph. The first choice above is the one you want.
User Neilakapete
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