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

Question

Responses

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

The parabola will open downwards.

Answer 1

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

1. Standard Form: The equation is in the form \( y = ax^2 + bx + c \), where:

   • \( a = -5 \)
   • \( b = 0 \)
   • \( c = 1 \)

2. Vertex: The vertex of a parabola in standard form can be found using the formula \( x = -\frac{b}{2a} \).

   • Here, \( x = -\frac{0}{2 \cdot -5} = 0 \).
   • To find the y-coordinate of the vertex, substitute \( x = 0 \) back into the equation: \[ y = -5(0)^2 + 1 = 1. \]
   • Thus, the vertex is at \( (0, 1) \).

3. Direction: Since \( a = -5 < 0 \), the parabola opens downward.

Now, let's review the provided statements based on this analysis:

• The parabola will have a vertex at \( (-1, 0) \). (Incorrect)
• The parabola will have a vertex at \( (0, 0) \). (Incorrect)
• The parabola will have a vertex at \( (1, 0) \). (Incorrect)
• The parabola will open downwards. (Correct)

The correct statement is: The parabola will open downwards.