Answer:
C
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) = (5, 2), thus
y = a(x - 5)² + 2
To find a substitute (4, - 3) into the equation
- 3 = a + 2 ⇒ a = - 3 - 2 = - 5
y = - 5(x - 5)² + 2 ← in vertex form
Expand (x - 5)² and distribute by - 5
y = - 5(x² - 10x + 25) + 2
= - 5x² + 50x - 125 + 2
= - 5x² + 50x - 123 ← in standard form