Graph the equation y=−5(x)2+1

Question

. 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 have a vertex at left parenthesis 1 comma 0 right parenthesis .

The parabola will open downwards.
The parabola will open downwards.

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)
.

Answer 1

The equation given is \( y = -5(x)^2 + 1 \). This represents a downward-opening parabola because the coefficient of \( x^2 \) is negative.

To find the vertex of the parabola, we can use the standard form of a quadratic equation, which is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola. In your equation, the vertex can be identified as follows:

1. The term \( -5(x)^2 \) indicates that the parabola is centered at \( x = 0 \) (since there is no horizontal shift).
2. The maximum value (the y-coordinate of the vertex) occurs when \( x = 0 \):

\[ y = -5(0)^2 + 1 = 1 \]

Thus, the vertex of the parabola is located at \( (0, 1) \).

Given the options, the correct statements regarding the graph of the parabola are:

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

Therefore, the correct statement about the graph is:

The parabola will open downwards.

Answer 2

Use the image to answer the question.

A coordinate plane shows an upward-opening parabola with a plotted point. Both axes range from negative 20 to 20 in increments of 5.

What is the vertex form of the graphed equation?

(1 point)
Responses

y=2(x+4)2+8
y equals 2 left parenthesis x plus 4 right parenthesis squared plus 8

y=2(x−4)2−8
y equals 2 left parenthesis x minus 4 right parenthesis squared minus 8

y=2(x−4)2+8
y equals 2 left parenthesis x minus 4 right parenthesis squared plus 8

y=−2(x−4)2+8