Questions: Roots for the Parabola Drag point A to move the parabola so that its roots are the two open blue points.

Transcript text: Roots for the Parabola Drag point A to move the parabola so that its roots are the two open blue points.

Solution

Solution Steps

Step 1: Identify the target roots

The two open blue points represent the target roots for the parabola. One point is at x = 2 and the other is at x = 6.

Step 2: Determine the required transformation

The current parabola has its vertex at (2,0), which makes x = 2 a repeated root. To include x=6 as a root, the parabola needs to be horizontally stretched.

Step 3: Determine the new vertex

The vertex of the parabola will lie midway between the roots at x=4. Its y-coordinate is unknown so we use the variable k. The new vertex is at (4, k) where k < 0.

Final Answer:

Move point A so that the vertex of the parabola sits at (4,k) where k < 0. This will cause the parabola to intercept the x-axis at the two blue points, x=2 and x=6. The exact value of k will depend on the specific program or tool being used.

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