Answer:
see explanation
Step-by-step explanation:
given a quadratic function with zeros x = a, x = b , then
the corresponding factors are (x - a ) and (x - b )
The equation is then the product of the factors, that is
y = a(x - a)(x - b) ← a is a multiplier
given a quadratic function with zeros x = 1 and x = 3 , then the factors are
(x - 1 ) and (x - 3 ), then
y = a(x - 1)(x - 3)
to find a, substitute (0, - 3) for x and y in the equation
- 3 = a(0 - 1)(0 - 3) = a(- 1)(- 3) = 3a ( divide both sides by 3 )
- 1 = a
y = - (x - 1)(x - 3) ← in factored form
expand the factors using FOIL
y = - (x² - 4x + 3) ← distribute parenthesis by - 1
y = - x² + 4x - 3 ← in standard form
