To analyze the quadratic function $f(x) = -2x^2 - 2x + 6$, let's determine the y-intercept and the axis of symmetry step by step:

1. Y-Intercept

The $y$-intercept of a function is the value of $f(x)$ when $x = 0$.

Substitute $x = 0$ into the function:

$f(0) = -2(0)^2 - 2(0) + 6 = 6$

Thus, the y-intercept is $(0, 6)$.

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2. Axis of Symmetry

The axis of symmetry for a quadratic function in the form $ax^2 + bx + c$ is given by the formula:

$x = -\frac{b}{2a}$

Here, $a = -2$ and $b = -2$. Substituting these values into the formula:

$x = -\frac{-2}{2(-2)} = \frac{2}{-4} = -\frac{1}{2}$

Thus, the axis of symmetry is $x = -\frac{1}{2}$.

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Final Answer:

• Y-Intercept: $(0, 6)$
• Axis of Symmetry: $x = -\frac{1}{2}$

Would you like additional details or clarification?

Here are some related questions you might explore:

1. How do you find the vertex of the given quadratic function?
2. Can you determine the maximum value of this quadratic function?
3. How would you graph this quadratic function?
4. What are the roots (if any) of this quadratic function?
5. How does changing the coefficient $a$ affect the graph of a quadratic function?

Tip: For quadratic functions, the vertex lies on the axis of symmetry, so finding the axis is a key step in graphing or analyzing the function.