Write an equation for the quadratic graphed below:
x-intercepts: (-2,0) and (1,0); y-intercept: (0,2)
Equation of quadratic function is:
y = a x² + b x + c = a ( x - x1 ) ( x - x2 )
where
a is leading coefficient
x1 an x2 are roots of this function
You know two roots:
x = - 2 , y = 0
and
x = 1 , y = 0
You function is:
y = a ( x - x1 ) ( x - x2 )
Since x1 = - 2 , x2= 1
y = a [ x - ( - 2 ) ] ( x - 1 )
y = a ( x + 2 ) ( x - 1 )
Now in this equation put value:
( 0 , 2 )
x = 0 , y = 2
y = a ( x + 2 ) ( x - 1 )
2 = a ( 0 + 2 ) ( 0 - 1 )
2 = a • 2 • ( - 1 )
2 = - 2 a
Divide both sides by - 2
- 1 = a
a = - 1
Your function is:
y = - ( x + 2 ) ( x - 1 )
Since ( x + 2 ) • ( x - 1 ) = x² + x - 2
y = - ( x + 2 ) ( x - 1) = - ( x² + x - 2 )
y = - x² - x + 2