This is an upward-facing parabola the axis of symmetry is a line of the form x = -a that is constant.
How to find the points symmetric over axes or origin?
Let the point be (x,y)
Case 1: Symmetry with respect to the x-axis
The point becomes (x, -y) as the point flips itself up or down which changes its y coordinate to the negative of whatever it was previously. And no motion is done horizontally so no change in x coordinate.
Case 2: Symmetry with respect to y-axis
The point becomes (-x, y) as the point flips itself left or right which changes its x coordinate to negative of whatever it was previously. And no motion is done vertically so no change in y coordinate.
Case 3: Symmetry with respect to origin
Origin is point at (0,0)
Symmetry with this is a bit ill defined. We use a slant line as if its a diagonal of a square.
The point is reflected to its diagonally opposite quadrant to whatever coordinate it belongs to.
Since diagonally opposite reflection causes both x and y axis to become negative of what it was before, thus,
The point becomes (-x,-y)
The axis of symmetry is where the left side is the mirror image of the right side.
Since this is an upward-facing parabola the axis of symmetry is a line of the form x = -a that is constant.
It will be the x coordinate of the vertex
x = 1
Learn more about symmetry here:
https://brainly.com/question/7783612
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