Given:

To solve the questions, evaluate each statement.
(a) The standard form of the equation.
The standard form of a quadratic equation is ax² + bx + c = 0. So, to find the standard form, subtract 3 from both sides of the equation.

So, the statement is correct.
(b) The factored form.
The factored form of a quadratic equation is (x-a)(x-b) = 0, where a and b are the zeros of the equations.
To find the zeros, use the quadratic formula.
For ax² + bx + c = 0, the zeros are:
![x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}^{}](https://img.qammunity.org/2023/formulas/mathematics/college/ely68nrv7g0zbj9kj7g644yie6175mj0r5.png)
So, substituting the values:
![\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-15)}}{2\cdot1}^{} \\ x=\frac{-2\pm\sqrt[]{4+60}}{2}^{}=\frac{-2\pm\sqrt[]{64}}{2} \\ x=(-2\pm8)/(2) \\ x_1=(-2-8)/(2)=-(10)/(2)=-5 \\ x_2=(-2+8)/(2)=(6)/(2)=3 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/w326w41w2r5r6viqspmo72ttpsgeqyn0yq.png)
The zeros are -5 and 3. So, the factored form is (x-3)(x+5) = 0
So, the statement is correct.
(c) Zero-Product Property.
Since (x-3)(x+5) = 0, then:
(x - 3) = 0
or
(x + 5) = 0
So, the statement is correct.
(d) Solutions of the equation.
The solutions of the equation are the zeros: -5 and 3 (shown in part B).
Thus, this statement is false. The correct would be the solution is -5 and 3.
(e) x-coordinate of the vertex.
The x-coordinate of the vertex is:

So, the statement is correct.
Answer: Statement D is wrong. The correct statement is: the solution is -5 and 3.