Answer:
y = 8x² - 160x + 793
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) = (10, - 7), hence
y = a(x - 10)² - 7
To find a substitute (3, 385) into the equation
385 = a(3 - 10)² - 7
385 = 49a - 7 ( add 7 to both sides )
392 = 49a ( divide both sides by 49 )
a = 8
y = 8(x - 10)² - 7 ← in vertex form
Expand the factors and simplify
y = 8(x² - 20x + 100) - 7
y = 8x² - 160x + 800 - 7
y = 8x² - 160x + 793 ← in standard form
