1) One strategy to verify that a quadratic function is in vertex form is to plot several points on the graph and see if they lie symmetrically around the vertex. In vertex form, the vertex of the parabola is given by the coordinates (h, k). By plugging in different values for x and calculating the corresponding y values, we can plot these points on a graph and observe if they follow a symmetrical pattern around the vertex. If the points are symmetric around the vertex, this indicates that the quadratic function is in vertex form.
2) Another strategy is to analyze the coefficients of the quadratic function. In vertex form, the quadratic function can be written as f(x) = a(x - h)^2 + k, where the variables a, h, and k represent the coefficients. The vertex form allows us to directly read the coordinates of the vertex, which are given by the values of h and k. By comparing the coefficients of the given quadratic function to the standard form of vertex form, we can check if they match. If the coefficients match, this confirms that the quadratic function is in vertex form.
3) A third strategy is to simplify the quadratic function to standard vertex form. To do this, we need to complete the square. By taking the given quadratic function and rewriting it in the form f(x) = a(x - h)^2 + k, we can then compare it to the vertex form. If the simplified quadratic function matches the vertex form, then it is in vertex form. This strategy allows us to directly calculate the coordinates of the vertex, which can be compared to the given quadratic function to verify if it is in vertex form.
Describe three different strategies you could use to verify that the quadratic function is in vertex form of the function.
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