Write the equation of the quadratic function with roots 0 and 2 and a vertex at (1, 5).

y = - 5(x - 1)² + 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

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

here (h, k) = (1, 5), hence

y = a(x - 1)² + 5

To find a substitute the coordinates of the root (2, 0) into the equation

0 = a + 5 ⇒ a = - 5

y = - 5(x - 1)² + 5 ← in vertex form

Expand (x - 1)² and rearrange

y = - 5(x² - 2x + 1) + 5

  = - 5x² + 10x - 5 + 5

y = - 5x² - 10x ← in standard form