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In the xy-plane, the graph of the equation y=3(x+6)^(2)+5 has a y-intercept of (0,b). What is the value of b ?

In the xy x y -plane, the graph of the equation y=3(x+6)2+5 y=3(x+6)^{2}+5 has a y y -intercept of (0,b) (0, b) . What is the value of b b ?

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Q. In the xy x y -plane, the graph of the equation y=3(x+6)2+5 y=3(x+6)^{2}+5 has a y y -intercept of (0,b) (0, b) . What is the value of b b ?
  1. Substitute x=0x = 0: To find the y-intercept of the graph, we need to substitute x=0x = 0 into the equation y=3(x+6)2+5y = 3(x + 6)^2 + 5 and solve for yy.
  2. Calculate value inside parentheses: Substitute x=0x = 0 into the equation: y=3(0+6)2+5y = 3(0 + 6)^2 + 5.
  3. Square the result: Calculate the value inside the parentheses: (0+6)=6(0 + 6) = 6.
  4. Multiply by 33: Square the result: 62=366^2 = 36.
  5. Add 55 to the result: Multiply by 33: 3×36=1083 \times 36 = 108.
  6. Find y-intercept: Add 55 to the result: 108+5=113108 + 5 = 113.
  7. Find y-intercept: Add 55 to the result: 108+5=113108 + 5 = 113.The y-intercept (0,b)(0, b) is where y=113y = 113 when x=0x = 0. Therefore, b=113b = 113.

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