Answer:
1. The equation of parabola is [tex]y=x^2-6x+5[/tex].
2. The equation of parabola is [tex]y=-2x^2+8x-8[/tex].
Step-by-step explanation:
1.
Let the equation of parabola be
[tex]y=ax^2+bx+c[/tex]
It is given that the parabola passing through points (0,5), (2,-3) and (-1,12).
[tex]5=a(0)^2+b(0)+c[/tex]
[tex]5=c[/tex]
The value of c is 5.
[tex]y=ax^2+bx+5[/tex]
The equation must be satisfied by the points (2,-3) and (-1,12).
[tex]-3=a(2)^2+b(2)+5[/tex]
[tex]-8=4a+2b[/tex]
Divide both sides by 2.
[tex]-4=2a+b[/tex] .... (1)
[tex]12=a(-1)^2+b(-1)+5[/tex]
[tex]7=a-b[/tex] .... (2)
From (1) and (2), we get
[tex]a=1,b=-6[/tex]
Therefore equation of parabola is [tex]y=x^2-6x+5[/tex].
2.
Let the equation of parabola be
[tex]y=ax^2+bx+c[/tex]
It is given that the parabola passing through points (2,0), (3,-2) and (1,-2).
[tex]0=a(2)^2+b(2)+c[/tex]
[tex]0=4a+2b+c[/tex] .... (3)
The equation must be satisfied by the points (3,-2) and (1,-2).
[tex]-2=a(3)^2+b(3)+c[/tex]
[tex]-2=9a+3b+c[/tex] .... (4)
[tex]-2=a(1)^2+b(1)+c[/tex]
[tex]-2=a+b+c[/tex] .... (5)
On solving (1), (2) and (3), we get
[tex]a=-2,b=8,c=-8[/tex]
Therefore equation of parabola is [tex]y=-2x^2+8x-8[/tex].
