Q:

# What is the method for graphing quadratic functions in vertex form?

A:

When a quadratic function is presented in vertex form, it contains within it the coordinates of the vertex or turning point of the function. Using this as the starting point of the graphing process, it is possible to then determine the width of the parabola and whether the function is concave (downwards) or convex (upwards). The vertex form is f(x) = a(x - h)^2 + k.

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In the vertex form, the coordinates of the turning point are (h, k), where "h" is the x coordinate and "k" is the y coordinate. The graphing process should begin at this point. The next step is to choose four values of x, two less than "h" and two greater than "h." Put these into the function, and then graph the results. This gives an indication of the shape of the parabola, which can then be extrapolated.

The shape of the parabola can also be determined from the vertex form. The sign of the multiplier "a" determines whether the function is concave or convex. If its sign is positive, the parabola of the function opens upwards from the vertex. If its sign is negative, the graph of the function opens downwards. The width of the parabola depends on the absolute value of the multiplier "a." For absolute values greater than 1, the parabola becomes narrower than the standard x-squared parabola. This is because the value of f(x) increases more quickly than it does in the standard parabola. When the absolute value of "a" is less than 1, the parabola becomes progressively broader as this value decreases. If the function is concave, then (h, k) is its maximum. If it is convex, (h, k) is its minimum.

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