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 given equation \( y = -5(x)^2 + 1 \), we can identify some important characteristics of the graph.

1. **Vertex**:
The equation is in the form \( y = ax^2 + bx + c \). In this case:
- \( a = -5 \)
- \( b = 0 \)
- \( c = 1 \)

For a parabola of the form \( y = a(x - h)^2 + k \), the vertex \((h, k)\) can be identified directly. Here, we can rewrite the equation as:
\[
y = -5(x - 0)^2 + 1
\]
This shows that the vertex is at \((0, 1)\).

2. **Direction**:
Because the coefficient of \( x^2 \) (which is \( -5 \)) is negative, we can determine that the parabola opens downwards.

Now, let's evaluate the statements:

- "The parabola will have a vertex at (1, 0)" → **False**
- "The parabola will have a vertex at (0, 0)" → **False**
- "The parabola will open downwards." → **True**
- "The parabola will have a vertex at (−1, 0)" → **False**

Thus, the correct statement about the graph is: **The parabola will open downwards.**