Math Problem Statement
f(x)=2x^2
Solution
The function you have provided is:
This is a quadratic function, where , and it has the general form , with and . Let's go over some key properties of this function:
-
Vertex: Since there is no linear term () or constant term (), the vertex is at the origin, .
-
Axis of symmetry: The axis of symmetry is the vertical line , which passes through the vertex.
-
Direction of the parabola: The coefficient of is positive, so the parabola opens upward.
-
Domain: The function is defined for all real values of , so the domain is .
-
Range: Since the parabola opens upward and the minimum value occurs at , the range is .
-
Growth rate: As increases or decreases away from 0, the value of grows quadratically, meaning it grows faster than a linear function.
Would you like more details or any specific questions answered?
Here are 5 related questions:
- How would the graph change if the coefficient of was negative?
- What are the intercepts of this quadratic function?
- How can the derivative of this function help describe its behavior?
- How does this quadratic compare to ?
- Can you express this function in vertex form, even though the vertex is already at the origin?
Tip: The coefficient of controls how "wide" or "narrow" the parabola is—larger values make the graph narrower.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Formulas
f(x) = ax^2 + bx + c
Theorems
Vertex Formula
Axis of Symmetry
Suitable Grade Level
Grades 8-10