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f(x) = x^2 + x − 6 Determine the x-intercepts and the y-intercept. And can you please explain how you got your answer

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Answer:

x - intercepts are x = - 3, x = 2 , y- intercept = - 6

Explanation:

the x- intercepts are the points on the x- axis where the graph of f(x) crosses the x- axis.

any point on the x- axis has a y- coordinate of zero.

let y = f(x) = 0 and solve for x, that is

x² + x - 6 = 0

consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)

the factors are + 3 and - 2 , since

3 × - 2 = - 6 and 3 - 2 = - 1 , then

(x + 3)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

x - 2 = 0 ( add 2 to both sides )

x = 2

the x- intercepts are x = - 3 and x = 2

the y- intercept is the point on the y- axis where the graph of f(x) crosses the y- axis.

any point on the y- axis has an x- coordinate of zero

let x = 0 in y = f(x)

f(0) = 0² + 0 - 6 = 0 + 0 - 6 = - 6

the y- intercept is y = - 6

User Awa Melvine
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