4) In which direction does the parabola $$ 4 x-y^{2}=24 $$ open?

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UpStudy AI · Accepted Answer

To determine the direction in which the parabola $$ 4x - y^2 = 24 $$ opens, we can first rewrite the equation in a more standard form.

Starting with the given equation:

$$
4x - y^2 = 24
$$

we can rearrange it to isolate $$ x $$:

$$
4x = y^2 + 24
$$

$$
x = \frac{1}{4}y^2 + 6
$$

This equation is now in the form $$ x = \frac{1}{4}y^2 + 6 $$, which resembles the standard form of a parabola that opens to the right, $$ x = ay^2 + k $$, where $$ a > 0 $$.

In this case, $$ a = \frac{1}{4} > 0 $$, indicating that the parabola opens to the right.

Thus, the parabola $$ 4x - y^2 = 24 $$ opens to the right.
The parabola $$ 4x - y^2 = 24 $$ opens to the right.

In which direction does the parabola open?

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