How ‘a’ Influences the Shape and Width of a Parabola in the Equation f(x) = a(x – h)^2 + k

What does the value of ‘a’ do? f(x)=a(x-h)^2+k

In the equation you provided, f(x) = a(x – h)^2 + k, ‘a’ represents the coefficient that determines the shape of the parabola

In the equation you provided, f(x) = a(x – h)^2 + k, ‘a’ represents the coefficient that determines the shape of the parabola. It is known as the coefficient of the quadratic term.

Here’s a breakdown of how ‘a’ influences the graph:

1. If ‘a’ is positive: When ‘a’ is positive, the parabola opens upwards, creating a U-shaped curve. The larger the value of ‘a’, the narrower the parabola becomes. If ‘a’ is equal to 1, the parabola has a standard shape. If ‘a’ is greater than 1, the parabola becomes narrower, and if ‘a’ is between 0 and 1, the parabola becomes wider.

2. If ‘a’ is negative: When ‘a’ is negative, the parabola opens downwards, resembling an inverted U-shape. Similar to the positive case, the magnitude of ‘a’ determines the width of the parabola. If ‘a’ is equal to -1, the parabola has a standard shape. If ‘a’ is less than -1, the parabola becomes narrower, and if ‘a’ is between 0 and -1, the parabola becomes wider.

In summary, the coefficient ‘a’ in the equation f(x) = a(x – h)^2 + k determines whether the parabola opens upward or downward and controls the shape and width of the curve.

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