Graph the equation y = -5(x)^2 + 1. Which of the following statements about the graph is correct?
A. The parabola will have a vertex at (-1, 0).
B. The parabola will have a vertex at (1, 0).
C. The parabola will open downwards.
D. The parabola will have a vertex at (0, 0).
The given equation is in the form of a quadratic equation, where the coefficient of x^2 is negative. Therefore, the parabola will open downwards.
The vertex of a quadratic equation in the form of y = a(x-h)^2 + k is given by the coordinates (h, k). In the given equation, the coefficient of x^2 is -5, so the vertex can be found by equating the x-coordinate to 0.
Putting x = 0 in the equation y = -5(x)^2 + 1, we get y = -5(0)^2 + 1 = 1.
Therefore, the parabola will have a vertex at (0, 1).
None of the options A, B, or D is correct.
The correct statement is:
C. The parabola will open downwards.