A quadratic relation has an equation of the form .
The graph of the relation has zeros at and and passes
through the point . Determine the value of .

Ask by Griffiths Santiago. in Canada

Mar 24,2025

Question

A quadratic relation has an equation of the form .
The graph of the relation has zeros at and and passes
through the point . Determine the value of .

Ask by Griffiths Santiago. in Canada

Mar 24,2025

UpStudy AI · Accepted Answer

1. The quadratic has the form 
   $$
   y = a(x-2)(x+6)
   $$
   since the zeros are at $$ x=2 $$ and $$ x=-6 $$.

2. Substitute the point $$ (3,5) $$ into the equation:
   $$
   5 = a(3-2)(3+6)
   $$

3. Simplify the expression:
   $$
   5 = a(1)(9) = 9a
   $$

4. Solve for $$ a $$:
   $$
   a = \frac{5}{9}
   $$
$$ a = \frac{5}{9} $$