graph each function and identify the vertex and axis of symmetry

g (x) = (x-2)^2 - 3

The function \( g(x) = (x - 2)^2 - 3 \) is a quadratic function in vertex form, which is given as:

\[
g(x) = a(x - h)^2 + k
\]

Here, \( h \) and \( k \) represent the vertex of the parabola, and the axis of symmetry is the vertical line \( x = h \).

### For the function \( g(x) = (x - 2)^2 - 3 \):
- \( h = 2 \)
- \( k = -3 \)

So, the vertex is \( (2, -3) \).

### Axis of symmetry:
The axis of symmetry is the vertical line that passes through the vertex, so it is:

\[
x = 2
\]

### Graph:
The parabola opens upwards since the coefficient of \( (x - 2)^2 \) is positive (the coefficient is 1), and the vertex is at \( (2, -3) \). The general shape will resemble a U-shaped curve with its lowest point at the vertex.

Would you like me to graph it for you?

---

Here are some additional questions to deepen understanding:
1. How does changing the value of \( h \) affect the graph of the function?
2. What happens if the coefficient in front of \( (x - 2)^2 \) changes to a negative number?
3. How can you find the y-intercept of the function \( g(x) \)?
4. How would the graph look if the function were \( g(x) = (x + 2)^2 - 3 \)?
5. How does the value of \( k \) influence the graph's vertical position?

**Tip**: The vertex form of a quadratic function makes it easy to identify the vertex and axis of symmetry, simplifying graphing tasks!

Graph each function and identify the vertex and axis of symmetry: g(x) = (x-2)^2 - 3

Learn how to graph the quadratic function g(x) = (x-2)^2 - 3 and identify its vertex and axis of symmetry. This problem uses the vertex form of a quadratic function and discusses the axis of symmetry. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation