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VMariaS [17]
3 years ago
5

Which direction does the graph of the equation shown below open?

Mathematics
2 answers:
Nonamiya [84]3 years ago
4 0

Answer:

A. Right

Step-by-step explanation:

Given

y^2-4x+4y-4=0

Isolating x

y^2 + 4y - 4 = 4x

(y^2)/4 + y - 1 = x

Which is a parabola in the single variable y. That means the curve may open to the right or to the left.

The y component of the vertex of the parabola (y_v)is calculated as

y_v = \frac{-b}{2 \times a}

where a is the coefficient of the quadratic term and b the coefficient of the linear term. Replacing in the formula:

y_v = \frac{-1}{2 \times 1/4} = -2

Replacing this value in the quadratic formula we get the x component of the vertex x_v

x_v = y_v^2/4 + y_v - 1

x_v = (-2)^2/4 + -2 - 1

x_v = -2

Now, we have to get another point in the curve. For example, taking y = 0, we get:

x  = (y^2)/4 + y - 1

x  = (0^2)/4 + 0 - 1

x = -1

Then, the points (-2, -2) and (-1, 0) belong to the parabola, and in consequence, it opens to the right (see figure attached).

Mnenie [13.5K]3 years ago
3 0
Option A.

you can rewrite the equation as x = y^2 / 4 + y - 1

If you conserve the traditional x-axis and y-axis, the parabola opens to the right (the symetry axis is parallel to x and the function grows as y grows).
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