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

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

Answer 1

To analyze the equation \( y = -5(x)^2 + 1 \), we can rewrite it in the standard form of a parabola, which is \( y = a(x-h)^2 + k \). In this form, the vertex of the parabola is given by the point \( (h, k) \).

1. Identify the vertex:
- Here, \( a = -5 \), which indicates that the parabola opens downwards.
- The vertex can be found by comparing it to the standard form:
- We can see that \( h = 0 \) and \( k = 1 \).
- Thus, the vertex is at the point \( (0, 1) \).

2. Determine the direction of the parabola:
- Since \( a = -5 \) (a negative value), the parabola opens downwards.

Now, let's evaluate each of the given statements:

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

The correct statement is:

**The parabola will open downwards.**