Math Problem Statement

Solve the system of equations: y = x^2 and y = 4.

Solution

It appears that the image contains some equations written as follows:

  1. y=x2y = x^2
  2. y=4y = 4

If you are asking how to solve or interpret these, it seems like two equations are provided:

  • The first equation, y=x2y = x^2, represents a parabola with vertex at the origin (0, 0), where yy is the square of xx.
  • The second equation, y=4y = 4, represents a horizontal line at y=4y = 4.

To find the points of intersection, we can set the two equations equal to each other since both represent yy:

x2=4x^2 = 4

This simplifies to:

x=±2x = \pm 2

Therefore, the points of intersection are x=2x = 2 and x=2x = -2, which correspond to the points (2,4)(2, 4) and (2,4)(-2, 4).

Let me know if you'd like further details or explanations!

Would you like to explore:

  1. The general properties of quadratic functions?
  2. How to graph these functions?
  3. Solving other system of equations?
  4. A deeper understanding of functions and their intersection points?
  5. The relationship between parabolas and lines?

Tip: When solving systems of equations, always check if both functions are linear or nonlinear, as that can affect the approach.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Graphing
Systems of Equations

Formulas

Quadratic equation: y = ax^2 + bx + c
Solving intersections: Set equations equal to each other

Theorems

Basic properties of quadratic functions
Intersection of a parabola and a line

Suitable Grade Level

Grades 8-10