Question

Write a quadratic that had x-intercepts of -2 and 1/3 show all of your steps

Answer 1

3x^2 + 5x - 2

Explanation:

In factor form this is:

(x + 2)(x - 1/3)

= x^2 - 1/3x + 2x - 2/3

= x^2 + 5/3 x = 2/3

Multiply through by 3:

= 3x^2 + 5x - 2 (answer).

Answer 2

y = 3x² + 5x - 2

Explanation:

Given the x- intercepts are x = - 2 and x =
`(1)/(3)`

Then the factors are (x + 2) and (x -
`(1)/(3)`)

The quadratic is the product of its factors, that is

y = a(x + 2)(x -
`(1)/(3)`) ← a is a multiplier

Expand the factors

y = a(x² +
`(5)/(3)` x -
`(2)/(3)`)

let a = 3

y = 3(x² +
`(5)/(3)` x -
`(2)/(3)`)

= 3x² + 5x - 2