Use the image to answer the question.

A parabola is graphed on a coordinate plane. The x-axis ranges from negative 10 to 3 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.

Which of the following is true based on the graph of the quadratic?

(1 point)
Responses

The c-value of the equation in standard form is −10
.
The c -value of the equation in standard form is negative 10 .

The a-value is negative.
The a -value is negative.

The c-value of the equation in standard form is −1
.
The c -value of the equation in standard form is negative 1 .

The vertex is located at (3,−10)

1 answer

To determine which statement is true regarding the graph of the parabola, we need to consider a few characteristics of parabolas:

  1. The c-value in the standard form of a quadratic equation \( y = ax^2 + bx + c \) represents the y-intercept of the graph, which is the point where the graph intersects the y-axis (when \( x = 0 \)).
  2. The a-value determines the direction (upwards if \( a > 0 \) and downwards if \( a < 0 \)) and the width of the parabola.
  3. The vertex of the parabola is its highest or lowest point, depending on the direction it opens.

From the information provided:

  • If the graph shows the parabola intersects the y-axis at (0, -10), then the c-value is indeed -10.
  • If the parabola opens downwards, the a-value is negative.
  • If the vertex is shown to be at (3, -10), that would contradict the typical calculations, as the vertex’s x-value being greater than the y-intercept at (0, -10) suggests a different location.

Based on these observations:

  1. If the parabola intersects the y-axis at (0, -10), then the c-value in standard form is -10 is true.
  2. If the parabola opens downwards (typical of a negative a-value), then the a-value is negative is also true.
  3. If the vertex is at (3, -10), this would likely be incorrect considering the location of the y-intercept unless it is defined as such by the specific graph.

To answer your query without visual confirmation, the most certain statement would likely be:

  • The c-value of the equation in standard form is −10.