In addition to translating the vertex of the parabola along the x axis, you can move it vertically, along the y axis. Toward this end, consider what happens if you add a constant k to the basic quadratic equation you have worked with in the previous sections. Here is the new form of the equation:

a(x – h)^{2} + k

This form of the equation allows you to adjust the y-intercept of the parabola. When you assign a value to k, you can translate the position of the vertex of the parabola up or down relative to the y axis.

As Figure 9.10 illustrates, if you assign a positive value to k, then you translate the vertex of the equation upward on the y axis. If the value of a is positive, then the vertex of the parabola opens upward, ...

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