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NISA [10]
2 years ago
13

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">
Enter your answer in the boxes.


(__ , __)
Mathematics
2 answers:
Artemon [7]2 years ago
6 0
I just took the test, the answer is actually (-2, 3)
OlgaM077 [116]2 years ago
3 0
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)
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mote1985 [20]

Answer:

c. f(x)=x(x+2)(x-1)(x-4)

Step-by-step explanation:

Where it says "as x goes to negative infinity" then "y goes to infinity" (that's the part with the infinity symbols) that means the graph is going up at it's left end. This curve is a quartic (4th degree) which means its left and right ends are kind of parabola-ish, but the middle is not the neat u-ish, v-ish shape of a parabola; it's more like a wonky, noodle-ish wavy affair. Anyway, LIKE a parabola when the beginning of the equation is positive, the two ends point up. That's what's happening here and so we can eliminate b. and d. as potential answers.

Since -2, 0, 1, 4 are zeros (which are solutions...and also x-intercepts) we can find the factors of the function.

If x = -2

ADD 2 to both sides.

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This means (x+2) is a factor.

This is enough info to select answer c. but let's verify the other factors.

If x = 1

SUBTRACT 1 from both sides.

x - 1 = 0

Thus means (x - 1) is a factor.

If x = 4

SUBTRACT 4 from both sides.

x - 4 = 0

(x - 4) is a factor.

You can see c. has all these factors as well as x, because x=0 already, so x is a factor too.

I think of this as a working backwards problem, bc usually you have to factor and solve. This one, you have solutions (which are zeros and x-intercepts) and work backwards to find factors and multiply them together to find the function.

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