Question

Write a quadratic function given the roots (3,0) and (-1,0) and the point (-3,3)?

Answer 1

a quadratic function given the roots (3,0) and (-1,0) and the point (-3,3)

when p and q are the roots    then we use equation

y = a(x- p)(x-q)

We are given with roots 3  and -1

y = a(x- 3)(x-(-1))

y = a(x- 3)(x + 1)

Now we use the given point (-3,3) to find out 'a'

3 = a(-3- 3)(-3 + 1)

3= a(-6)(-2)

3= 12a

divide by 12 on both sides

$a= \frac{1}{4}$

Replace the value of 'a'

$f(x)= \frac{1}{4}(x-3)(x+1)$