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

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.