Using the following equation, find the vertex and axis of symmetry. y=2x^2+12x-11

To find the vertex and axis of symmetry for the quadratic equation \( y = 2x^2 + 12x - 11 \), we follow a similar process:

### 1. **Identify the coefficients:**
The equation is in the form \( y = ax^2 + bx + c \), where:
- \( a = 2 \)
- \( b = 12 \)
- \( c = -11 \)

### 2. **Find the axis of symmetry:**
The axis of symmetry for the parabola is given by:

\[
x = -\frac{b}{2a}
\]

Substituting the values of \( a \) and \( b \):

\[
x = -\frac{12}{2(2)} = -\frac{12}{4} = -3
\]

So, the axis of symmetry is \( x = -3 \).

### 3. **Find the vertex:**
The vertex lies on the axis of symmetry. To find the \( y \)-coordinate of the vertex, substitute \( x = -3 \) into the original equation:

\[
y = 2(-3)^2 + 12(-3) - 11
\]
\[
y = 2(9) - 36 - 11
\]
\[
y = 18 - 36 - 11 = -29
\]

So, the vertex of the parabola is \( (-3, -29) \).

### **Summary:**
- **Vertex:** \( (-3, -29) \)
- **Axis of Symmetry:** \( x = -3 \)

Would you like more details or have any questions?

### Related Questions:
1. How can you graph a quadratic equation using the vertex and axis of symmetry?
2. What is the significance of the vertex in the context of a real-world problem?
3. How do you determine the direction of the parabola's opening?
4. Can the quadratic equation be factored to find the roots?
5. What is the relationship between the vertex and the maximum/minimum value of the function?
6. How would completing the square help in finding the vertex?
7. What is the y-intercept of the given quadratic function?
8. How would you find the x-intercepts of the parabola?

**Tip:** The vertex can also be found by completing the square, which can sometimes provide more insight into the nature of the quadratic function.

Discover how to find the vertex and axis of symmetry for the quadratic equation y = 2x^2 + 12x - 11. Follow a step-by-step explanation including the quadratic formula, axis of symmetry calculation, and vertex determination. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation