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In this example, the a-value equals 2. What changes when you change the b-value? What stays the same?

Question

In this example, the a-value equals 2.

  • What changes when you change the b-value?
  • What stays the same?
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Solution

The question seems to be referring to a function, possibly a quadratic function in the form of y = ax^2 + bx + c. However, without more context, it's difficult to provide a specific answer.

Generally, in such a function:

  1. The 'a' value affects the direction and the width of the parabola. If 'a' is positive, the parabola opens upwards, and if 'a' is negative, it opens downwards. The absolute value of 'a' determines the width of the parabola.

  2. The 'b' value affects the position of the vertex of the parabola along the x-axis. Changing 'b' will move the graph left or right along the x-axis.

  3. The 'c' value affects the position of the graph along the y-axis. Changing 'c' will move the graph up or down.

So, if you change the 'b' value while keeping 'a' constant at 2, the shape and direction of the parabola will remain the same, but its position along the x-axis will change. The vertex of the parabola will move left or right.

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