Question

Write the equation for a parabola that has x− intercepts (−1.6,0) and (−3.2,0) and y−intercept (0,25.6).

Answer 1

X-intercepts are zeroes of the parabola.
(x-x1)(x-x2)=(x+1.6)(x+3.2)=x² +1.6x+3.2x+5.12=x²+4.8x+5.12
 
y=x²+4.8x+5.12, but the y-int. is (0, 25.6),

So, our parabola should look like
y=5(x²+4.8x+5.12)
y=5x²+24x+25.6

Answer 2

 Answer: y = 5(x + 1.6)(x + 3.2)

∞∞∞∞∞∞∞∞
Explanation:
∞∞∞∞∞∞∞∞

x-intercept = (-1.6, 0) and (-3.2, 0)

=====>   y = a(x + 1.6)(x + 3.2)

Given y-intercept = (0, 25.6)

=====>  25.6 = a( 0 + 1.6)(0 + 3.2) 
=====>  25.6 = 5.12a
=====>  a = 5

Plug in a = 5 into the equation

=====>  y = 5(x + 1.6)(x + 3.2)