Answer:
[1].
Option A and D are correct.
[2].
Option A is correct
Step-by-step explanation:
[1].
Quadratic function states that it is an equation of second degree i.,e it contains at least one term that is squared.
The standard form of the quadratic equation is; ![ax^2+bx+c = 0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%20%3D%200)
A.
![y(y+4)-y = 6](https://tex.z-dn.net/?f=y%28y%2B4%29-y%20%3D%206)
Using distributive property: ![a\cdot (b+c) = a\cdot b + a\cdot c](https://tex.z-dn.net/?f=a%5Ccdot%20%28b%2Bc%29%20%3D%20a%5Ccdot%20b%20%2B%20a%5Ccdot%20c)
![y^2+4y-y=6](https://tex.z-dn.net/?f=y%5E2%2B4y-y%3D6)
Combine like terms;
![y^2+3y = 6](https://tex.z-dn.net/?f=y%5E2%2B3y%20%3D%206)
or
which represents a quadratic equation.
B.
![3a-7 = 2(7a-3)](https://tex.z-dn.net/?f=3a-7%20%3D%202%287a-3%29)
![3a-7 = 14a-6](https://tex.z-dn.net/?f=3a-7%20%3D%2014a-6)
or
which is not a quadratic equation.
C.
(3x+2)+(6x-1) = 0
Combine like terms;
9x +1 = 0 which is not a quadratic equation.
D.
4b(b) = 0
which represents the quadratic equation.
[2].
Given the parent function: ![y=x^2](https://tex.z-dn.net/?f=y%3Dx%5E2)
The reflection rule over x axis is given by;
![(x, y) \rightarrow (x, -y)](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%5Crightarrow%20%28x%2C%20-y%29)
then
the function become: ![y = -x^2](https://tex.z-dn.net/?f=y%20%3D%20-x%5E2)
Vertical shift:
If c is a positive real number, the graph y=f(x)+c is the graph of y =f(x) shifted upward c units.
If c is a positive real number, the graph y=f(x)-c is the graph of y =f(x) shifted downward c units.
then;
The graph
is the graph of
shifted 3 units down.
Therefore, the translation of the graph of
to obtain
is, reflect over the x-axis and shift down 3