Math Problem Statement

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

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

Solution

The graph you have provided shows a parabola that opens upwards. The "zeros" of a parabola, also known as the x-intercepts, are the points where the parabola crosses the x-axis. These points represent the solutions to the quadratic equation corresponding to the parabola.

From the graph, the parabola intersects the x-axis at two points. By inspecting the graph, the approximate coordinates of the zeros are:

  • x=5x = 5
  • x=7x = 7

So, the zeros of the parabola are at the points (5,0)(5, 0) and (7,0)(7, 0).

Would you like to go over details of this analysis, or do you have any questions?

Here are 5 questions related to the graph and zeros of parabolas:

  1. How can you determine the equation of a parabola if you know its zeros?
  2. What does the vertex of this parabola tell you about the quadratic equation?
  3. How are the zeros of the parabola related to its axis of symmetry?
  4. What is the significance of the direction in which the parabola opens?
  5. Can a parabola have more than two zeros? Why or why not?

Tip: The vertex of a parabola lies exactly midway between its two zeros, providing important information about its axis of symmetry.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Zeros of Parabolas

Formulas

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

Theorems

Properties of quadratic equations
Relationship between zeros and the vertex

Suitable Grade Level

Grades 9-12