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The parabola f() = ² - 12 + 32 is in the form f() = a(-h)² + k. Find and interpret the value of a.

User Pankmish
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Final answer:

The value of a in the equation of a parabola determines its shape and orientation. In this case, a = 1, indicating that the parabola opens upwards and is relatively wide.

Step-by-step explanation:

The parabola function f(x) = x^2 - 12x + 32 is given in the form f(x) = a(-h)^2 + k, where a is the leading coefficient and (-h, k) is the vertex of the parabola. To find the value of a, we compare the given function with the general form of a parabola and identify the values of a, h, and k. In this case, a = 1 since the coefficient of x^2 is 1. So, the value of a is 1.

Interpreting the value of a, it tells us that the parabola opens upwards (since a > 0) and is relatively wide (since a = 1), meaning the graph is not very steep.

User Gregory Boutte
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