Question

Write the equation of the line, given the y and x-intercepts.

y-intercept = –6, x-intercept = –2

Answer 1

Linear equation: (-2,-6)

Quadratic Equation: y =
`x^2` +8x =12

Explanation:

see Example image #1 for Linear Equation graph

See Example image #2 for Quadratic Equation graph

Quadratic Equation Explanation:

x = -2 an x = -6 are the two real distinct solutions for the quadratic equation, which means that x+2 and x+6 are the factors of the quadratic equation.

( x + 2 ) ( x + 6 ) = 0

Expand ( x + 2 ) ( x + 6 ) using the FOIL Method.

x ⋅ x + x ⋅ 6 + 2 x + 2 ⋅ 6 = 0

Simplify and combine like terms.

`x^2` + 8 x + 12 = 0

The standard quadratic equation using the given set of solutions{ − 2 , − 6 } is

y =
`x^2` + 8 x + 12 .