Graph the parabola. Identify the vertex.

Question

yequalsnegative 2 x squared
Question content area bottom
Part 1
Choose the correct graph below.
A.
-5
5
-25
25
x
y

x y graph
B.
-5
5
-25
25
x
y

x y graph
C.
-5
5
-25
25
x
y

x y graph
D.
-5
5
-25
25
x
y

x y graph
Your answer is correct.
Part 2
What is the​ vertex?
  
enter your response here ​(Type an ordered​ pair.)

Answer 1

To graph the parabola given by the equation \( y = -2x^2 \), we can identify key features such as the vertex and the shape of the parabola.

Step 1: Identify the Vertex

The equation \( y = -2x^2 \) is in the standard form of a quadratic equation \( y = ax^2 + bx + c \), where:

• \( a = -2 \)
• \( b = 0 \)
• \( c = 0 \)

The vertex of a parabola in standard form \( y = ax^2 + bx + c \) can be calculated using the formula for the x-coordinate of the vertex: \[ x = -\frac{b}{2a} \] Substituting our values: \[ x = -\frac{0}{2(-2)} = 0 \] Next, we find the y-coordinate by substituting \( x = 0 \) back into the equation: \[ y = -2(0)^2 = 0 \] Thus, the vertex is at the point \( (0, 0) \).

Step 2: Graph the Parabola

Since the coefficient of \( x^2 \) is negative, the parabola opens downwards. The vertex at \( (0, 0) \) is the highest point on the graph. You can choose several values of \( x \) to find corresponding \( y \) values to sketch the parabola:

• If \( x = 1 \): \( y = -2(1)^2 = -2 \) → point \( (1, -2) \)
• If \( x = -1 \): \( y = -2(-1)^2 = -2 \) → point \( (-1, -2) \)
• If \( x = 2 \): \( y = -2(2)^2 = -8 \) → point \( (2, -8) \)
• If \( x = -2 \): \( y = -2(-2)^2 = -8 \) → point \( (-2, -8) \)

Parabola Behavior

The graph is symmetric about the y-axis, with the vertex at the highest point.

Part 2 - Vertex Response

The vertex of the parabola \( y = -2x^2 \) is: \[ (0, 0) \]

Conclusion

Choose the graph that has a vertex at \( (0, 0) \) and opens downwards, and the vertex of the parabola is \( (0, 0) \).