opens downward equation when the downward graph's points are on the left is -5, on the right is 5, and on top is 5. The only options you can choose are below with a max of choosing 2. y = 4, x = 4, x = -4, x = -3, x = 3

Answer 1

To create an equation of a downward-opening parabola that fits the specified conditions, we need to understand the implications of the points provided.

The points indicate that the graph's top (vertex) is at the point (0, 5), and it opens downward. The points on the left and right are -5 and 5, which suggest that those are the x-intercepts.

The problem can be broken down as follows:

1. Vertex: The graph has its vertex at \( (0, 5) \).
2. X-intercepts: The x-intercepts are at \( x = -5 \) and \( x = 5 \).

Given this data, the general form of a downward-opening parabola can be represented as: \[ y = a(x - h)^2 + k \] where \( (h, k) \) is the vertex. For our case, \( h = 0 \) and \( k = 5 \), so the equation simplifies to: \[ y = a(x^2) + 5 \]

To determine the value of \( a \), we can use one of the x-intercepts. Let's use the x-intercept at \( x = 5 \): When \( y = 0 \) (at the x-intercepts): \[ 0 = a(5^2) + 5 \] \[ 0 = 25a + 5 \] \[ 25a = -5 \] \[ a = -\frac{1}{5} \]

Now substituting \( a \) back into our equation: \[ y = -\frac{1}{5}x^2 + 5 \]

This is the equation of the downward-opening parabola.

However, since you provided specific options (y = 4, x = 4, x = -4, x = -3, x = 3) and you mentioned selecting a maximum of two options, it seems like you are looking for specific points or additional constraints. Since the parabola intersects the line \( y = 4 \), we can derive the x-values from the equation we established.

Setting \( y = 4 \): \[ 4 = -\frac{1}{5}x^2 + 5 \] \[ x^2 = 5 - 4 \cdot -5 \] \[ x^2 = 5(-1) \] This does not lead us within the provided options, but it gives us insight into how the y-values can contrast with the specifically stated x-values.

In summary, while you cannot select a fitting equation or options strictly using your conditions and the specific answer choices provided. Only one of the selections aligns symmetrically with a parabola under conditions of \(-4\) or \(4\).

Thus, out of the options, we recognize that your specified downward-opening parabola is best manifested with the equation derived \(y = -\frac{1}{5}x^2 + 5\), which meets your x-edge conditions.

If you need further work to interpret selections that fit or clarify more math, please let me know!