y

It looks like you're trying to write a mathematical equation. Based on your input, it appears you intended to write:

$y = 2x^2 - 4$

This represents a quadratic equation. Here, $y$ is expressed as a function of $x$. The general form of a quadratic function is:

$y = ax^2 + bx + c$

where:

• $a = 2$ (the coefficient of $x^2$),
• $b = 0$ (there is no linear $x$ term),
• $c = -4$ (the constant term).

Key Features of the Quadratic Function

1. Vertex: The vertex form of a parabola $y = ax^2 + bx + c$ can be found using the vertex formula $x = -\frac{b}{2a}$. In this case, the vertex is at $(0, -4)$.
2. Axis of Symmetry: The axis of symmetry for the parabola is a vertical line that passes through the vertex. Here, it is $x = 0$.
3. Direction of Opening: Since $a = 2 > 0$, the parabola opens upwards.
4. Y-Intercept: The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation gives $y = -4$. So, the y-intercept is $(0, -4)$.
5. X-Intercepts: The x-intercepts occur when $y = 0$. Setting the equation to 0:

$0 = 2x^2 - 4 \implies 2x^2 = 4 \implies x^2 = 2 \implies x = \pm \sqrt{2}$

So, the x-intercepts are at $x = \sqrt{2}$ and $x = -\sqrt{2}$.

Would you like more details on any of these features or have any questions?

Related Questions:

1. How do you find the vertex of a quadratic function in different forms?
2. What is the significance of the discriminant in a quadratic equation?
3. How can you convert a standard form of a quadratic equation to its vertex form?
4. How do transformations affect the graph of a quadratic function?
5. What are the steps to solve quadratic equations using the quadratic formula?

Tip: Always check the coefficient of the $x^2$ term in a quadratic function to determine whether the parabola opens upwards or downwards.