Question

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

Answer 1

Answer:

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

$y=-x^{3}$

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

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

$y=x^{4}$

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

Answer 2

I think y=x2+6x+9 hope this helps