$$ \# 30 y = x ^ { 2 } - 2 x ; x _ { 0 } = - 1 $$

Question

UpStudy AI · Accepted Answer

It looks like you're providing the equation:

$$
y = x^2 - 2x \quad \text{with an initial value} \quad x_0 = -1
$$

Assuming you want to evaluate $$ y $$ at $$ x_0 = -1 $$, here's how you can do it:

$$
y = (-1)^2 - 2(-1) = 1 + 2 = 3
$$

**So, when $$ x = -1 $$, the value of $$ y $$ is 3.**

---

**Additional Context (If Relevant):**

If you're looking to analyze this function further, such as finding its roots or exploring its behavior, here's a brief overview:

1. **Roots of the Equation $$ y = x^2 - 2x $$:**
   
   To find the values of $$ x $$ where $$ y = 0 $$:
   
   $$
   x^2 - 2x = 0 \
   x(x - 2) = 0
   $$
   
   So, the roots are:
   
   $$
   x = 0 \quad \text{and} \quad x = 2
   $$

2. **Vertex of the Parabola:**
   
   Since the equation is a quadratic in the form $$ y = ax^2 + bx + c $$, the vertex can be found using:
   
   $$
   x = -\frac{b}{2a} = -\frac{-2}{2 \times 1} = 1
   $$
   
   Plugging $$ x = 1 $$ back into the equation:
   
   $$
   y = (1)^2 - 2(1) = 1 - 2 = -1
   $$
   
   So, the vertex is at $$ (1, -1) $$.

3. **Graph Behavior:**
   
   - The parabola opens upwards since the coefficient of $$ x^2 $$ is positive.
   - It intersects the y-axis at $$ y = 0 $$ when $$ x = 0 $$.
   - The vertex represents the minimum point of the parabola.

If you have a specific question or a different context in mind regarding this equation, feel free to provide more details!
When $$ x = -1 $$, $$ y = 3 $$.

\( \# 30 y = x ^ { 2 } - 2 x ; x _ { 0 } = - 1 \)

Solución de tutoría real

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Algebra Questions