To find the vertex and the line of symmetry of the quadratic function $y = -2x^2 - 4x + 6$, we can follow these steps:

1. Identify the coefficients

The quadratic equation is in the form: $y = ax^2 + bx + c$ For this equation:

• $a = -2$
• $b = -4$
• $c = 6$

2. Calculate the x-coordinate of the vertex

The x-coordinate of the vertex is given by the formula: $x = -\frac{b}{2a}$ Substitute the values of $a$ and $b$: $x = -\frac{-4}{2(-2)} = \frac{4}{-4} = -1$

3. Calculate the y-coordinate of the vertex

Substitute $x = -1$ back into the original equation to find the y-coordinate: $y = -2(-1)^2 - 4(-1) + 6$ $y = -2(1) + 4 + 6 = -2 + 4 + 6 = 8$ So, the vertex is at $(-1, 8)$.

4. Find the equation of the line of symmetry

The line of symmetry is a vertical line that passes through the vertex. The equation of the line of symmetry is: $x = -1$

Final Answer:

• Vertex: $(-1, 8)$
• Line of Symmetry: $x = -1$

Would you like further details or have any questions?

Here are some related questions:

1. How does the sign of the coefficient $a$ affect the direction of the parabola?
2. What is the y-intercept of the given quadratic function?
3. How do you find the x-intercepts (roots) of the quadratic function?
4. Can you convert the given quadratic function to its vertex form?
5. What does the vertex represent in the context of a quadratic function?

Tip: The vertex form of a quadratic equation can be useful for quickly identifying the vertex and direction of the parabola.