Question

What is the focus of the parabola? xFormula1" title="y= \frac{1}{4} x^{2} -x+3" alt="y= \frac{1}{4} x^{2} -x+3" align="absmiddle" class="latex-formula">
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Answer 1

I just took the test, the answer is actually (-2, 3)

Answer 2

We know that
the equation of the parabola is of the form
y=ax²+bx+c
in this problem
y=1/4x²−x+3
where
a=1/4
b=-1
c=3
 the coordinates of the focus are
(-b/2a,(1-D)/4a)
where D is the discriminant b²-4ac
D=(-1)²-4*(1/4)*3-----> D=1-3---> D=-2
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> 2

y coordinate of the focus
(1-D)/4a------> (1+2)/(4/4)---> 3

the coordinates of the focus are (2,3)