Answer:
y = 2x² - 3x + 5
Step-by-step explanation:
substitute the coordinates of the points the curve passes through into the equation.
using (0, 5 )
5 = a(0)² + b(0) + c
5 = 0 + 0 + c
5 = c
y = ax² + bx + 5
using (1, 4 )
4 = a(1)² + b(1) + 5 ( subtract 5 from both sides )
a + b = - 1 → (1)
using (- 2, 19 )
19 = a(- 2)² + b(- 2) + 5 ( subtract 5 from both sides )
14 = 4a - 2b , that is
4a - 2b = 14 → (2)
multiplying (1) by 2 and adding to (2) will eliminate b
2a + 2b = - 2 → (3)
add (2) and (3) term by term to eliminate b
6a + 0 = 12
6a = 12 ( divide both sides by 6 )
a = 2
substitute a = 2 into (1) and solve for b
2 + b = - 1 ( subtract 2 from both sides )
b = - 3
Then equation of curve is
y = 2x² - 3x + 5
