Question

Which of the following is an equatic

Answer 1

Answer:

y = - x² + 4x + 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

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

Here (h, k) = (2, 5), thus

y = a(x - 2)² + 5

To find a substitute (- 1, - 4) into the equation

- 4 = a(- 1 - 2)² + 5 = a(- 3)² + 5 = 9a + 5 ( subtract 5 from both sides )

9a = - 9 ( divide both sides by 9 )

a = - 1

y = - (x - 2)² + 5 ← in vertex form

Expanding and simplifying

y = - (x² - 4x + 4) + 5

  = - x² + 4x - 4 + 5

   = - x² + 4x + 1 ← in standard form