What are the characteristics of the graph of the parabola f(x) =  – (x – 1)^2 + 4

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the parabola given is : f(x) = –(x – 1)^2 + 4

The standard form of the parabola y = a*(x - h)^2 + k can be used to determine all its characteristics.

Here, a is negative, indicating that the parabola opens upwards.

The vertex is at (h, k). For the equation given it is (1, 4)

The the axis of symmetry is x = 4

The x-intercepts are determined by solving –(x – 1)^2 + 4 = 0

=> x = -1 and x = 3

The x-intercepts are (-1, 0) and (3, 0)

The y-intercept is (0, f(0)) which here is (0, 3)

The domain of the parabola is all the values that x can take for real values of y. Here it is R.

The range of the parabola is all the values y can take for x lying in the domain. Here it is [-inf., 4]

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