Linear algebra (Matrices)

Question

The equation for a parabola has the form y=ax² +bx+c where a ,b and, c are constants and a≠0 Find an equation for the parabola that passes through the points (3,9), (1,5) and (4,17)

Answer 1

The equation for a parabola has the form y=ax² +bx+c where a ,b and, c are constants and a≠0 Find an equation for the parabola that passes through the points (3,9), (1,5) and (4,17)

As the Parabola passes through ( 3,9)

X = 3 , Y = 9

plug in the equation

9 = 9a +3b + c ....... Eq 1

Next point (1,5)

.

X= 1, Y = 5

5 = a + b + c ........ Eq 2

Third point

(4,17 )

X = 4, Y = 17

17 = 16a + 4b +c ..... Eq 3

Sove these three Equation for a, b and c

By substitution 8a + 2b = 4 and 15a +3b = 12

a= 2 , b = 3

c = -18

Equation of parabola is

y= 2X² +3X-18

Please check the answer and inform me , if you have a questioin