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N76 [4]
3 years ago
10

COMPLETE THE SQUARE TO REWRITE Y=X>2+8X+3 IN VERTEX FORM , AND THEN IDENTIFY THE MINIMUN Y-VALUE OF THE FUNCTION

Mathematics
1 answer:
kicyunya [14]3 years ago
6 0

Answer:

The vertex form is y = (x + 4)² - 13

The minimum value of the function is -13

Step-by-step explanation:

∵ y = x² + 8x + 3

∵ 8x ÷ 2 = 4x ⇒ (x) × (4)

∴ We need ⇒ x² + 8x + 16 to be completed square

∴ y = (x² + 8x + 16) - 16 + 3 ⇒ we add 16 and subtract 16

∴ y = (x + 4)² - 13 ⇒ vertex form

∵ The vertex form is (x - a)² + b

Where a is the x-coordinate of the minimum point and b is y-coordinate of the minimum point (b is the minimum value of the function)

∴ The minimum value is -13

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<span>           x                            x
-----------------  -  --------------------
x^2 -4x + 4            </span><span>x^2-3x+2

</span>           x                            x
= ----------------  -  --------------------
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        x (x-1)  - x(x +2)                       
= ----------------------------
          (x -2)^2 (x - 1)

      x^2 -x -x^2 - 2x                    
= --------------------------
      (x -2)^2 (x - 1)

           -3x                    
= -----------------------
      (x -2)^2 (x - 1)

answer 
<span>missing term in the equation: -3x</span>
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