Math Problem Statement

Using the graph, find p(4) and find x such that p(x) = -3.

Solution

From the graph provided, we need to solve for two things:

  1. Find p(4)p(4):
    To find p(4)p(4), locate x=4x = 4 on the x-axis and check the corresponding value of p(x)p(x) (the y-coordinate of the graph at x=4x = 4).

    From the graph, at x=4x = 4, the corresponding point on the parabola is (4,3)(4, -3).
    Therefore, p(4)=3p(4) = -3.

  2. Find xx such that p(x)=3p(x) = -3:
    To find xx where p(x)=3p(x) = -3, we look at where the graph intersects the line y=3y = -3.

    The graph intersects the horizontal line y=3y = -3 at two points: x=2x = 2 and x=4x = 4.
    Therefore, the values of xx such that p(x)=3p(x) = -3 are x=2x = 2 and x=4x = 4.

Summary:

  • p(4)=3p(4) = -3
  • x=2x = 2 and x=4x = 4 when p(x)=3p(x) = -3.

Would you like more details or have any further questions?


Here are some related questions to deepen your understanding:

  1. What is the vertex of the parabola shown in the graph?
  2. Can you determine the axis of symmetry from the graph?
  3. How would you write the equation of the parabola based on the graph?
  4. What is the maximum or minimum value of p(x)p(x) from the graph?
  5. If p(x)p(x) represents a real-world scenario, how could you interpret p(4)=3p(4) = -3?

Tip: When reading values from a graph, be sure to check both the x and y coordinates carefully to avoid mistakes.

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Math Problem Analysis

Mathematical Concepts

Quadratic Functions
Graph Interpretation

Formulas

-

Theorems

Intersection of a quadratic function and horizontal line

Suitable Grade Level

Grades 7-9