Math Problem Statement

Using the graph, determine the coordinates of the zeros of the parabola.

Solution

To find the coordinates of the zeros (also called roots or x-intercepts) of the parabola shown in the graph, we need to identify where the curve intersects the x-axis.

In this graph, the parabola crosses the x-axis at two points:

  • One on the left, approximately at x=6x = -6
  • The other on the right, approximately at x=1x = 1

Thus, the coordinates of the zeros are: (6,0)and(1,0)(-6, 0) \quad \text{and} \quad (1, 0)

Would you like more details or have any questions about how I determined this?

Here are 5 additional related questions:

  1. What does the vertex of a parabola represent?
  2. How can you determine if the parabola opens upwards or downwards?
  3. What is the equation of the axis of symmetry for this parabola?
  4. How can we find the exact roots of a quadratic function algebraically?
  5. What is the significance of the discriminant in finding the roots of a quadratic equation?

Tip: When identifying zeros from a graph, make sure to check where the graph exactly intersects the x-axis, as these are the points where y=0y = 0.

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Math Problem Analysis

Mathematical Concepts

Parabola
Zeros of a Quadratic Function
Graph Interpretation

Formulas

Quadratic equation formula ax^2 + bx + c = 0

Theorems

Zeros of a function

Suitable Grade Level

Grades 8-10