The coordinates of the focus of the parabola are (2, -1.9375)
How to determine the focus?
The equation of the parabola is given as:
[tex]y = \frac 14x^2 - x - 1[/tex]
Express as a vertex form
[tex]y = \frac 14(x - 2)^2 - 2[/tex]
The focus of a quadratic function of the form [tex]y = a(x - h)^2 + k[/tex] is
Focus = (h, k + 1/4 a)
By comparing [tex]y = a(x - h)^2 + k[/tex] and [tex]y = \frac 14(x - 2)^2 - 2[/tex], we have:
a = 1/4
h = 2
k = -2
So, we have:
Focus = (2, -2 + 1/4 * 1/4)
Evaluate
Focus = (2, -1.9375)
Hence, the coordinates of the focus of the parabola are (2, -1.9375)
Read more about parabolas at:
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