Questions: Which way does the equation (y=-x^2 +4) open?

Transcript text: Which way does the equation $y=-x^{2}$ +4 open?

Solution

Solution Steps

Hint

The direction in which a parabola opens is determined by the sign of the coefficient of the $x^2$ term in the quadratic equation. If this coefficient is negative, the parabola opens downwards.

Step 1: Identify the Coefficient of $x^2$ Term

The given equation is $y = -x^2 + 4$. The coefficient of the $x^2$ term is $-1$.

Step 2: Determine the Direction Based on the Coefficient

The direction in which a parabola opens is determined by the sign of the coefficient of the $x^2$ term. If the coefficient is negative, the parabola opens downwards. In this case, the coefficient is $-1$, which is negative.