The text in the image reads:

"Graph the parabola y = x² - 2x + 1. What is the axis of symmetry?"

Solution:

1. Equation Simplification: The equation $y = x^2 - 2x + 1$ is already in standard form:
   $y = ax^2 + bx + c$ where $a = 1$, $b = -2$, and $c = 1$.

2. Vertex and Axis of Symmetry: The formula for the axis of symmetry of a parabola is:
   $x = -\frac{b}{2a}$
   Substituting $a = 1$ and $b = -2$:
   $x = -\frac{-2}{2(1)} = \frac{2}{2} = 1$
   So, the axis of symmetry is $x = 1$.

3. Graphing Steps:

   • The vertex is at $(1, 0)$, calculated by substituting $x = 1$ into the equation:
     $y = (1)^2 - 2(1) + 1 = 0$

   • Additional points can be found by choosing values of $x$ around $x = 1$:

     • For $x = 0$: $y = 0^2 - 2(0) + 1 = 1$
     • For $x = 2$: $y = 2^2 - 2(2) + 1 = 1$

     Points: $(0, 1)$, $(1, 0)$, $(2, 1)$.

   • The parabola is symmetric about $x = 1$ and opens upwards since $a > 0$.

4. Axis of Symmetry: The axis of symmetry is $x = 1$.

Would you like me to graph the parabola or explain any steps in more detail?

Related Questions:

1. How do you find the vertex of a parabola given its equation?
2. What is the significance of the coefficient $a$ in a parabola's equation?
3. How does the value of $b$ in $ax^2 + bx + c$ affect the axis of symmetry?
4. How can you determine if a parabola opens upwards or downwards?
5. Can you find the equation of the parabola if the vertex and a point are given?

Tip:

Always check if the quadratic equation can be factored easily. In this case, $x^2 - 2x + 1$ is $(x - 1)^2$, which reveals the vertex directly.