Answer:
y = - 2(x - 2)² - 3
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) = (2, - 3) , thus
y = a(x - 2)² - 3
To find a substitute (1, - 5) a point on the curve into the equation
- 5 = a(1 - 2)² - 3
- 5 = a - 3 ⇒ a = - 5 + 3 = - 2
y = - 2(x - 2)² - 3 ← equation in vertex form
