Quadratic function MC question?

Question

A quadratic function with roots 4/5 and 4/3 would be:

A) y = 15x^2 + 8x - 16
B) y = 15x^2 - 32x + 16
C) y = 15x^2 + 32x + 16
D) y = 15x^2 - 8x - 16

Answer 1

Start with (x - 4/5) and (x - 4/3)

Multiply the first times 5 to remove the fraction:
(5x - 4)

...and the second times 3 to remove the fraction:
(3x - 4)

Now multiply them out:
First: 5x * 3x = 15x²
Outer: 5x * -4 = -20x
Inner: 3x * -4 = -12x
Last: -4 * -4 = 16

Add it all up:
15x² - 20x - 12x + 16

Combine the x terms:
15x² - 32x + 16

The answer is B.

Answer 2

Roots 4/5 and 4/3 would mean that
x = 4/5
and
x = 4/3

in quadratic form that would give:
(x - 4/5)(x - 4/3)

expanding it would give:
(x^2 - (4/3)x - (4/5)x + 16/15)

standardizing the denominators by multiplying each term by 15:
(15x^2 - 15( 20/15 + 12/15)x + 16)

Finally:
15x^2 - 32x + 16

so the answer would be B!

Answer 3

B) y = B) y = 15x^2 - 32x + 16
bcoz
(x-4/5)(x-4/3)= 15x^2 - 32x + 16
x = 4/5 x= 4/3

Answer 4

i have no idea