Question

or
The equation of a parabola is y=x2–10x+25. Write the equation in vertex form.
Write any numbers as integers or simplified proper or improper fractions.

Answer 1

To convert the equation of the parabola \( y = x^2 - 10x + 25 \) into vertex form, we can complete the square.

1. **Start with the given equation**:

\[
y = x^2 - 10x + 25
\]

2. **Identify the quadratic and linear terms**: The quadratic term is \( x^2 \) and the linear term is \( -10x \).

3. **Complete the square**:

- Take the coefficient of \( x \), which is \(-10\), divide it by 2, and square it:
\[
\left(\frac{-10}{2}\right)^2 = (-5)^2 = 25
\]

- Rewrite the equation:
\[
y = (x^2 - 10x + 25)
\]

- Factor the perfect square:
\[
y = (x - 5)^2
\]

4. **Therefore, the equation in vertex form is**:

\[
y = (x - 5)^2
\]

In this form, you can see that the vertex of the parabola is at the point \( (5, 0) \).