Graph the equation y=−5(x)2+1

Question

. Which of the following statements about the graph is correct?(1 point)
Responses

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

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

Answer 1

To analyze the equation \( y = -5(x)^2 + 1 \), let's identify key features of its graph:

1. Direction of Opening:

   • The coefficient of \( x^2 \) is \(-5\), which is negative. Therefore, the parabola opens downwards.

2. Vertex:

   • The standard form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex.
   • In this equation, we can see that it can be rewritten to identify the vertex more clearly: \[ y = -5(x - 0)^2 + 1 \]
   • Here, \( h = 0 \) and \( k = 1 \), which gives the vertex at \((0, 1)\).

Given these observations, we can evaluate the provided statements:

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

Conclusion: The correct statement is "The parabola will open downwards."