Answer:
https://socratic.org/questions/how-do-you-write-the-equation-of-the-quadratic-function-with-roots-6-and-10-and-
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Given the roots are x = 6 and x = 10, then
the factors are (x - 6) and (x - 10)
The quadratic is then the product of the roots
y = a(x - 6)(x - 10) ← a is a multiplier
To find a substitute (8, 2) into the equation
2 = a(2)(- 2) = - 4a ( divide both sides by - 4 )
a = - [tex]\frac{1}{2}[/tex]
Hence
y = - [tex]\frac{1}{2}[/tex](x - 6)(x - 10) ← expand factors
y = - [tex]\frac{1}{2}[/tex](x² - 16x + 60) ← distribute
y = - [tex]\frac{1}{2}[/tex] x² + 8x - 30
