Math Problem Statement
Solution
The problem asks for the equation of the function , which has the same shape as the given function but is shifted up by 3 units.
To find the equation of , we start with the base function . When a function is shifted vertically by 3 units, we add 3 to the function:
Since , we substitute this into the equation:
Thus, the equation for is:
Would you like further details or have any questions?
Here are 5 related questions:
- What would happen if the function was shifted down by 3 units?
- How does shifting horizontally affect the function equation?
- What does the vertex of the parabola represent after the vertical shift?
- Can you describe how the graph of differs from ?
- How would you shift the function to the left or right?
Tip: When graphing, vertical shifts affect the -coordinates, while horizontal shifts modify the -coordinates.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Graphing Functions
Transformations of Functions
Quadratic Functions
Formulas
g(x) = f(x) + k
g(x) = x^2 + 3
Theorems
Vertical Translation
Suitable Grade Level
Grades 7-9
Related Recommendation
Graph Quadratic Functions and Transformations: f(x) = x^2 and g(x) = (x - 3)^2
Understanding Function Shifts: Horizontal and Vertical Shifts of Quadratic Functions
Vertical Shift of Function g(x) = f(x) + 3 Based on Graph of f(x)
Vertical Shifts of Quadratic Functions: y = x^2 + k
Determine g(x) After Shifting f(x) = x^2 Vertically