A parabola has x-axis intercepts 6 and -3, and passes through the point (1,10). Find the equation of the parabola.

y=-1/2 x^2+3/2 x+9

Step-by-step explanation:

The equation of parabola is:

y=ax^2+bx+c

We know that parabola has three poibts

(6,0),(-3,0) and (1,10).

So we put these three points in equation:

a*36+b*6+c=0......(1)

a*9-3b+c=0........(2)

a+b+c=10........(3)

(1)-(2) we have:

27a+9b=0.....(4)

(2)-(3) we have:

8a-4b=-10.....(5)

4(4)+9(5) we got:

180a=-90

a=-1/2

From (4) we got: b=27/18=3/2

From (3) we got: c=10+1/2-3/2=9

So equation is:

y=-1/2 x^2+3/2 x+9

You can see the picture of parabola through three points.