Question

draw the parabolas axis of symmetry.

Explanation:

Step1: Recall the property of the axis of symmetry

The axis of symmetry of a parabola passes through the vertex and is equidistant from any two symmetric points on the parabola.

Step2: Locate the symmetric points

In the given graph, the two blue - colored points are symmetric. Let the coordinates of the left - hand blue point be \((x_1,y)\) and the right - hand blue point be \((x_2,y)\). Here, \(x_1=-4\) and \(x_2 = 4\).

Step3: Calculate the axis of symmetry

The formula for the axis of symmetry (for a horizontal line of symmetry of two points \((x_1,y)\) and \((x_2,y)\)) is \(x=\frac{x_1 + x_2}{2}\). Substitute \(x_1=-4\) and \(x_2 = 4\) into the formula: \(x=\frac{-4 + 4}{2}=0\)

The axis of symmetry is the \(y\) - axis (\(x = 0\)). So, draw a vertical line along the \(y\) - axis (the line \(x = 0\)) on the coordinate plane.

Answer:

Step1: Recall the property of the axis of symmetry

The axis of symmetry of a parabola passes through the vertex and is equidistant from any two symmetric points on the parabola.

Step2: Locate the symmetric points

In the given graph, the two blue - colored points are symmetric. Let the coordinates of the left - hand blue point be \((x_1,y)\) and the right - hand blue point be \((x_2,y)\). Here, \(x_1=-4\) and \(x_2 = 4\).

Step3: Calculate the axis of symmetry

The formula for the axis of symmetry (for a horizontal line of symmetry of two points \((x_1,y)\) and \((x_2,y)\)) is \(x=\frac{x_1 + x_2}{2}\). Substitute \(x_1=-4\) and \(x_2 = 4\) into the formula: \(x=\frac{-4 + 4}{2}=0\)

The axis of symmetry is the \(y\) - axis (\(x = 0\)). So, draw a vertical line along the \(y\) - axis (the line \(x = 0\)) on the coordinate plane.