Question

Find the equation of the parabola that passes through the points

Answer 1

Answer:

1.  The equation of parabola is $y=x^2-6x+5$.

2. The equation of parabola is $y=-2x^2+8x-8$.

Step-by-step explanation:

1.

Let the equation of parabola be

$y=ax^2+bx+c$

It is given that the parabola passing through points (0,5), (2,-3) and (-1,12).

$5=a(0)^2+b(0)+c$

$5=c$

The value of c is 5.

$y=ax^2+bx+5$

The equation must be satisfied by the points (2,-3) and (-1,12).

$-3=a(2)^2+b(2)+5$

$-8=4a+2b$

Divide both sides by 2.

$-4=2a+b$                         .... (1)

$12=a(-1)^2+b(-1)+5$

$7=a-b$                            .... (2)

From (1) and (2), we get

$a=1,b=-6$

Therefore equation of parabola is $y=x^2-6x+5$.

2.

Let the equation of parabola be

$y=ax^2+bx+c$

It is given that the parabola passing through points (2,0), (3,-2) and (1,-2).

$0=a(2)^2+b(2)+c$

$0=4a+2b+c$                      .... (3)

The equation must be satisfied by the points (3,-2) and (1,-2).

$-2=a(3)^2+b(3)+c$  

$-2=9a+3b+c$                     .... (4)

$-2=a(1)^2+b(1)+c$

$-2=a+b+c$                            .... (5)

On solving (1), (2) and (3), we get

$a=-2,b=8,c=-8$

Therefore equation of parabola is $y=-2x^2+8x-8$.