Question

The equation of a parabola is y=x^2–4x+13. Write the equation in vertex form.

Simplify any fractions.

Answer 1

vertex form : y=(x-2)^2+9

Explanation:

To convert a parabola from standard form y=x^2-4x+13 to vertex form, we complete the square.

first, complete the square using the x-terms, use the constant term to adjust and make a perfect square.

y= x^2-4x+4 + 9

Factor the first three terms on the right-hand side.

y=(x-2)^2 + 9

the resulting express is then the vertex form, which means that

the vertex is at (x-2) = 0, x=2, and at y=9.

Answer 2

y = (x - 2)² + 9

Explanation:

To obtain the equation in vertex form use the method of completing the square.

Add/ subtract ( half the coefficient of the x- term)² to x² - 4x

y = x² + 2(- 2)x + 4 - 4 + 13

= (x - 2)² + 9 ← in vertex form