Which of these equations has a graph that is tangent to the x-axis at one of its intercepts? Choose all the polynomials that have this property.

y = x^2 + 6x + 9

y = - x^3

y = (x + 2) (x + 6) ^2

y = (x - 5) (x + 3) (x + 1) (x - 5)

y = x^4

Question

Mathematics

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14 August, 05:14

Which of these equations has a graph that is tangent to the x-axis at one of its intercepts? Choose all the polynomials that have this property.

y = x^2 + 6x + 9

y = - x^3

y = (x + 2) (x + 6) ^2

y = (x - 5) (x + 3) (x + 1) (x - 5)

y = x^4

+5

Answers (1)

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Douglas Mcmahon · Answer 1

An equation is tangent to the x-axis when it has an even number of a certain root. A root is a value of x that results to a value of y = 0.

The first equation has roots - 3, and - 3. The graph will be tangent to the x-axis along with third, the fourth, and the fifth equation by the same condition that they have roots with even multiplicity (repeated in an even number of ways).

Which of these equations has a graph that is tangent to the x-axis at one of its intercepts? Choose all the polynomials that have this property.y = x^2 + 6x + 9y = - x^3y = (x + 2) (x + 6) ^2y = (x - 5) (x + 3) (x + 1) (x - 5)y = x^4

Which of these equations has a graph that is tangent to the x-axis at one of its intercepts? Choose all the polynomials that have this property.

y = x^2 + 6x + 9

y = - x^3

y = (x + 2) (x + 6) ^2

y = (x - 5) (x + 3) (x + 1) (x - 5)

y = x^4