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Use the graph of the parabola to fill in the table.

Use the graph of the parabola to fill in the table.

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Find the axis of symmetry of a parabolaright chevron icon

Full solution

Q. Use the graph of the parabola to fill in the table.
  1. Identify Equation Form: Identify the form of the equation. The equation x=12(y+3)2+5x = \frac{1}{2}(y + 3)^2 + 5 is in the form x=a(y−k)2+hx = a(y - k)^2 + h, which is a horizontal parabola.
  2. Determine Vertex: Determine the vertex (h,k)(h, k) of the parabola. Comparing x=12(y+3)2+5x = \frac{1}{2}(y + 3)^2 + 5 with the standard form, we get h=5h = 5 and k=−3k = -3.
  3. Find Axis of Symmetry: Find the axis of symmetry. For a horizontal parabola, the axis of symmetry is a vertical line through the vertex, so it's y=ky = k.
  4. Substitute for Axis: Substitute the value of kk into y=ky = k to get the axis of symmetry. So, the axis of symmetry is y=−3y = -3.

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