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
Here (h, k) = (3, 1), hence
y = a(x - 3)² + 1
To find a substitute (- 2, - 4) into the equation
- 4 = a(- 2 - 3)² + 1
- 4 = 25a + 1 ( subtract 1 from both sides )
25a = - 5 ( divide both sides by 25 )
a = - [tex]\frac{5}{25}[/tex] = - [tex]\frac{1}{5}[/tex]
y = - [tex]\frac{1}{5}[/tex] (x - 3)² + 1 ← in vertex form
