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If the equation y=x^(2)+9 is graphed in the xy-plane, what are the coordinates of the vertex of the graph? Choose 1 answer: (A) (-3,0) (B) (0,3) (c) (0,9) (D) (9,0)

If the equation y=x2+9 y=x^{2}+9 is graphed in the xy x y -plane, what are the coordinates of the vertex of the graph?\newlineChoose 11 answer:\newline(A) (−3,0) (-3,0) \newline(B) (0,3) (0,3) \newline(C) (0,9) (0,9) \newline(D) (9,0) (9,0)

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Full solution

Q. If the equation y=x2+9 y=x^{2}+9 is graphed in the xy x y -plane, what are the coordinates of the vertex of the graph?\newlineChoose 11 answer:\newline(A) (−3,0) (-3,0) \newline(B) (0,3) (0,3) \newline(C) (0,9) (0,9) \newline(D) (9,0) (9,0)
  1. Parabola Opens Upwards: The equation y=x2+9y = x^2 + 9 is a parabola in standard form, where the coefficient of x2x^2 is positive, indicating that the parabola opens upwards.
  2. Standard Form of a Parabola: The standard form of a parabola is y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola. In the given equation, y=x2+9y = x^2 + 9, there is no (x−h)(x - h) term, which means h=0h = 0.
  3. Determining the Vertex: Since there is no (x−h) (x - h) term and the equation is y=x2+9 y = x^2 + 9 , we can see that the k k value is 9 9 . This gives us the y y -coordinate of the vertex.
  4. Vertex of the Parabola: Combining the values of hh and kk, we find that the vertex of the parabola is at the point (h,k)=(0,9)(h, k) = (0, 9).

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