Question

Which statement best describes the graph of f(x)=-x^4+3x^3+10x^2

Answer 1

Answer:

option-B

Step-by-step explanation:

We are given function as

$f(x)=-x^4+3x^3+10x^2$

we know that

Any function touches or crosses x-axis when y-value is 0

so, we can set f(x)=0

and then we can solve for x

$f(x)=-x^4+3x^3+10x^2=0$

now, we can factor it

$-x^2(x^2-3x-10)=0$

$-x^2(x-5)(x+2)=0$

we get

$-x^2=0$

$x=0$

It means that function touches x-axis at x=0

$(x-5)(x+2)=0$

$(x-5)=0$

$x=5$

$(x+2)=0$

$x=-2$

So, function crosses x-axis at x=5 and x=-2

so,

option-B

Answer 2

Answer:

The graph touches the x-axis at x=0 and crosses the x-axis at x=5 and x=-2.

Step-by-step explanation:

We have the following function and we are to solve it for x:

$f(x)=-x^4+3x^3+10x^2$

We will put the given function equal to zero and solve it as we know that the function crosses the x-axis when y = 0.

$-x^4+3x^3+10x^2=0$

So taking the common terms out:

$-x^2(x^2-3x-10)=0$

$-x^{2} (x-5)(x+2)=0$

$-x^{2} =0, x=0$

$(x-5)=0, x=5$

$(x+2)=0, x=-2$

Therefore, the graph touches the x-axis at x=0 and crosses the x-axis at x=5 and x=-2.