Question

Graph the equation y=−5(x)^2+1
. Which of the following statements about the graph is correct?(1 point)
Responses

The parabola will have a vertex at (1,0)
.
The parabola will have a vertex at left parenthesis 1 comma 0 right parenthesis .

The parabola will have a vertex at (0,0)
.
The parabola will have a vertex at left parenthesis 0 comma 0 right parenthesis .

The parabola will open downwards.
The parabola will open downwards.

The parabola will have a vertex at (−1,0)
.

Answer 1

To analyze the equation \( y = -5(x)^2 + 1 \), we can identify key features of the parabola:

1. **Vertex**: The general form of a parabola given by \( y = a(x-h)^2 + k \) has its vertex at the point \((h, k)\). In your equation, it can be rewritten in vertex form as \( y = -5(x - 0)^2 + 1 \). This means that the vertex is at \((0, 1)\).

2. **Direction**: The coefficient of the quadratic term (\(a = -5\)) indicates the direction of the parabola. Since \(a\) is negative, the parabola opens downwards.

Now, let's analyze the statements provided:

1. The parabola will have a vertex at \( (1,0) \). **(Incorrect)**
2. The parabola will have a vertex at \( (0,0) \). **(Incorrect)**
3. The parabola will have a vertex at \( (-1,0) \). **(Incorrect)**
4. The parabola will open downwards. **(Correct)**

The correct statement is: **The parabola will open downwards.**