Rewrite the quadratic function in vertex form.
y=5x^2-10x+2

y = 5(x - 1)² - 3

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

• The coefficient of the x² - term must be 1

Factor out 5 from the first 2 terms

y = 5(x² - 2x) + 2

• add/subtract (half the coefficient of the x- term)² to x² - 2x

y = 5(x² + (- 1)x + (- 1)² - (- 1)² ) + 2 ← complete the square

y = 5(x - 1)² - 5 + 2

y = 5(x - 1)² - 3 ← in vertex form

both equations and proportions are better.