Math Problem Statement

is y=-x^2+3 considered a function

Solution

Yes, y=x2+3y = -x^2 + 3 is considered a function.

In mathematics, a function is defined as a relation where each input (in this case, xx) is assigned to exactly one output (in this case, yy). For the equation y=x2+3y = -x^2 + 3, for every value of xx, there is only one corresponding value of yy. This satisfies the definition of a function.

Additionally, this is a quadratic function, where the highest degree of xx is 2, and the graph of this function would be a parabola that opens downwards due to the negative sign in front of x2x^2.

Would you like further details on functions or quadratic equations?

Here are 5 related questions for deeper exploration:

  1. How can you determine whether a relation is a function using the vertical line test?
  2. What are the key characteristics of quadratic functions?
  3. How can you find the vertex of the parabola represented by y=x2+3y = -x^2 + 3?
  4. What is the domain and range of the function y=x2+3y = -x^2 + 3?
  5. How do you find the roots or x-intercepts of a quadratic function?

Tip: When analyzing a quadratic function like y=x2+3y = -x^2 + 3, note that its vertex gives the maximum or minimum value of the function depending on whether it opens upwards or downwards.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Quadratic Functions

Formulas

y = ax^2 + bx + c (Quadratic Function Form)

Theorems

Definition of a Function
Vertical Line Test

Suitable Grade Level

Grades 8-10