Answer:
see explanation
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
(1)
(h, k) = (1, - 4)
y = a(x - 1)² - 4
to find a use any other point that lies on the graph and substitute the coordinates into the equation
using (0, - 3), then
- 3 = a(- 1)² - 4
- 3 = a - 4 ⇒ a = - 3 + 4 = 1
y = (x - 1)² - 4 ← equation in vertex form
(2)
(h, k) = (1, - 10)
y = a(x - 1)² - 10 → using (3, - 2)
- 2 = 4a - 10 ⇒ 4a = 8 ⇒ a = 2
y = 2(x - 1)² - 10 ← equation in vertex form
(3)
(h, k) = (2, 1)
y = a(x - 2)² + 1 → using (3, 0)
0 = a + 1 ⇒ a = - 1
y = -(x - 2)² + 1 ← equation in vertex form
