Define the formula for a parabola a quadratic function that

Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x=3.6 and x = 4.8 and passes through the point (0,1.3) .

Solution

the equation of the parabola is y = ax^2 +bx+c

given

x= 4.8 and x=3.6 are horizontal intercepts

that means

0 = a(4.8)^2 +b(4.8) +c

a(23.04) +b(4.8) +c=0

and for x=3.6

a(3.6)^2 +b(3.6) +c=0

a(12.96) +b(3.6) +c=0

and it is passing through (0,1.3)

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

so we got c= 1.3

plug in the above equation we got

a(23.04) +b(4.8) +1.3=0

a(12.96) +b(3.6)+1.3=0

solving

a =-0.06

b=-0.26

parabola is y = -0.06^2 -.26x + 1.3