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
