Question

Pls answer I have an exam tmr

The curve y = ax^2 + bx+c passes through the points (1,4), (-2, 19) and (0,5). Find the equation of the curve.​

Answer 1

y = 2x² - 3x + 5

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