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 open downwards.

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

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

Answer 1

After analyzing the influence of philosophers on the American Framers of the U.S. Constitution, choose which of the following is given credit for the idea of separation of powers for government.(1 point)
Responses

Washington
Washington

Montesquieu
Montesquieu

Rousseau
Rousseau

Hobbes

Answer 2

To analyze the equation \( y = -5(x)^2 + 1 \):

1. This is a quadratic equation in the form of \( y = ax^2 + bx + c \), where \( a = -5 \), \( b = 0 \), and \( c = 1 \).
2. The vertex of a parabola in standard form is located at \( (h, k) \), where \( h = -\frac{b}{2a} \) and \( k = f(h) \).
3. In this case, since \( b = 0 \) and \( a = -5 \), we have:
\[
h = -\frac{0}{2 \cdot (-5)} = 0
\]
4. To find \( k \), we can substitute \( h \) back into the equation:
\[
k = -5(0)^2 + 1 = 1
\]
5. Thus, the vertex is at \( (0, 1) \).

Regarding the direction of the parabola:
- Since \( a = -5 < 0 \), the parabola opens **downwards**.

Now let's evaluate the statements given:
- **The parabola will have a vertex at (−1,0)**: Incorrect.
- **The parabola will open downwards**: Correct.
- **The parabola will have a vertex at (0,0)**: Incorrect.
- **The parabola will have a vertex at (1,0)**: Incorrect.

The correct statement is: **The parabola will open downwards.**