Question

Write the equation of the quadratic function with roots 6 and 10 and a vertex at (8, 2).

Answer 1

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 2

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 = - $\frac{1}{2}$

Hence

y = - $\frac{1}{2}$(x - 6)(x - 10) ← expand factors

y = - $\frac{1}{2}$(x² - 16x + 60) ← distribute

y = - $\frac{1}{2}$ x² + 8x - 30