Mathematics: 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 = x2 + 6x + 9 y = –x3 y = (x + 2)(x + 6)2 y = (x – 5)(x + 3)(x + 1)(x – 5) y = x4

Which of these equations has a graph that is tangent

tina7659

11.01.2022

$y=x^{2}+6x+9$

$y=-x^{3}$

$y=(x+2)(x+6)^{2}$

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

$y=x^{4}$

Step-by-step explanation:

we know that

If the graph is tangent to the x-axis at one of its intercepts

then

the vertex of the graph or the inflection point of the graph lie on the x-axis

using a graphing tool

Verify each case

case A) $y=x^{2}+6x+9$

The case A) has a graph that is tangent to the x-axis at one of its intercepts

case B) $y=-x^{3}$

The case B) has a graph that is tangent to the x-axis at one of its intercepts

case C) $y=(x+2)(x+6)^{2}$

The case C) has a graph that is tangent to the x-axis at one of its intercepts

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

The case D) has a graph that is tangent to the x-axis at one of its intercepts

case E) $y=x^{4}$

The case E) has a graph that is tangent to the x-axis at one of its intercepts

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