Quadratic Functions in Standard Form Quick Check

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Question
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 vertex is located at (3,−10)
The vertex is located at left parenthesis 3 comma negative 10 right parenthesis

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
.

1 answer

Based on the description of the graph and the given options, here's how to evaluate each statement:

  1. The vertex is located at (3, −10): This can only be true if the parabola indeed has its vertex at the coordinate (3, -10).

  2. The c-value of the equation in standard form is −10: The c-value represents the y-intercept of the quadratic function in standard form \(y = ax^2 + bx + c\). If the parabola reaches the y-value of −10 at x = 0, then this statement would be true.

  3. The a-value is negative: If the parabola opens downwards, then the a-value is negative. If it opens upwards, the a-value is positive.

  4. The c-value of the equation in standard form is −1: This contradicts the earlier statement about the c-value being −10.

Without the specific visual from the image, I can't definitively say which statement is true. However, you should analyze the graph based on these descriptions:

  • Check the coordinates of the vertex to affirm or deny the first statement.
  • Identify the value where the parabola intersects the y-axis to determine the c-value.
  • Observe the direction of the parabola to evaluate whether the a-value is negative or positive.

If the parabola opens downwards, the a-value is negative, which would make that statement true. Choose the option that aligns with your analysis of the graph.