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

Question

Responses

The parabola will open downwards.

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

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

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

Answer 1

To analyze the equation \( y = -5x^2 \):

1. Identify the parabola direction: Since the coefficient of \( x^2 \) is negative (-5), the parabola opens downwards.

2. Determine the vertex: This equation is in the standard form of a parabola \( y = ax^2 + bx + c \) where \( a = -5 \), \( b = 0 \), and \( c = 0 \). The vertex of a parabola in this form is at \( (h,k) \) where \( h = -\frac{b}{2a} \) and \( k = f(h) \). Here, \( b = 0 \), so \( h = -\frac{0}{2 \cdot -5} = 0 \). Thus, the x-coordinate of the vertex is 0. Plugging \( x = 0 \) into the equation gives \( y = -5(0)^2 = 0 \). Therefore, the vertex is at \( (0,0) \).

Now, considering the statements provided:

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

Final conclusions: The correct statements about the graph are that the parabola will open downwards and the parabola will have a vertex at (0,0).