For a function to be even, it must satisfy the equality 

Likewise if a function is even, it is symmetrical about the y-axis 

Therefore, the function is not even, and so the answer is No

For a function to be symmetrical about the y-axis, it must satisfy   so there is not symmetry about the y-axis

For a function to be symmetrical about the x-axis, it must satisfy   so there is symmetry about the x-axis

For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

-So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis

For a function to be symmetrical about the y-axis, it must satisfy  so there is symmetry about the y-axis

For a function to be symmetrical about the x-axis, it must satisfy  

 so there is not symmetry about the x-axis

For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

So there is no symmetry about the origin.

For a function to be symmetrical about the y-axis, it must satisfy 

 so there is symmetry about the y-axis

For a function to be symmetrical about the x-axis, it must satisfy 

 so there is not symmetry about the x-axis

For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

So there is no symmetry about the origin, and the credited answer is "symmetry about the y-axis".

For a function to be symmetrical about the y-axis, it must satisfy 

 so there is not symmetry about the y-axis

For a function to be symmetrical about the x-axis, it must satisfy 

 so there is symmetry about the x-axis

For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x), and the resulting function must be equal to the original function.

So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis.

For a function to be even, it must satisfy the equality

Likewise, if a function is even, it is symmetrical about the y-axis

Therefore, the function is not even, and so the answer is No.

If the roots of the equation are at x= -4 and x=3, then we can work backwards to see what equation those roots were derived from. If we factored a quadratic equation and obtained the given solutions, it would mean the factored form looked something like:

Because this is the form that would yield the solutions x= -4 and x=3. If we work backwards and multiply the factors back together, we get the following quadratic equation:

We can make a quadratic polynomial with  by mutiplying the linear polynomials they are roots of, and multiplying them out.

Start

Distribute the negative sign

FOIL the two polynomials. This means multiply the firsts, then the outers, followed by the inners and lastly, the last terms.

Simplify

Since we know the solutions of the equation, we know that:

We simply carry out the multiplication on the left side of the equation to get the quadratic equation.

These two points tell us that the quadratic function has zeros at , and at .

These correspond to the linear expressions , and .

Expand their product and you arrive at the correct answer.

If the quadratic is opening up the coefficient infront of the squared term will be positive. Thus we get:

.

If the quadratic is opening down it would pass through the same two points but have the equation:

.

Since only  is seen in the answer choices, it is the correct answer.