In the realm of mathematics, understanding the relationship between a function and its graph is crucial. Write an equation for the function graphed above presents a systematic approach to unraveling this connection, empowering you to transform visual representations into precise mathematical expressions.
Through a comprehensive analysis of the graph’s shape, intercepts, and key characteristics, this guide will equip you with the tools to determine the underlying function equation. Delve into the intricacies of linear, quadratic, and exponential functions as we explore the methodologies for finding coefficients and parameters that perfectly align with the given graph.
Graph Analysis
The graph is a parabola that opens upwards. The x-axis is labeled “x” and the y-axis is labeled “y”. The graph has a y-intercept at (0, 2) and an x-intercept at (1, 0).
Function Equation
The equation for the parabola is y = x^2 + 2.
Example Table
| x | y |
|---|---|
| 0 | 2 |
| 1 | 3 |
| 2 | 6 |
Methodologies, Write an equation for the function graphed above
To find the equation of the parabola, we can use the following steps:
- Identify the vertex of the parabola. The vertex is the point where the parabola changes direction.
- Use the vertex to find the axis of symmetry of the parabola. The axis of symmetry is a vertical line that passes through the vertex.
- Use the vertex and the axis of symmetry to write the equation of the parabola in vertex form.
Additional Notes
The graph of the parabola is symmetric about the y-axis. This means that the equation of the parabola can also be written in the following form: y = (x – h)^2 + k, where (h, k) is the vertex of the parabola.
FAQ Section: Write An Equation For The Function Graphed Above
How do I determine the type of function that fits a graph?
Examine the graph’s shape and key features. Linear functions exhibit straight lines, quadratic functions form parabolas, and exponential functions display curved lines that either increase or decrease rapidly.
What are the steps involved in finding the equation of a linear function?
Identify the slope and y-intercept from the graph. The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.
How do I find the coefficients of a quadratic function?
Use the vertex form of the quadratic equation: y = a(x – h)^2 + k, where (h, k) is the vertex. Determine the vertex from the graph and substitute it into the equation to find the value of a.
