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; [tex]ax^2+bx+c = 0[/tex]
A.
[tex]y(y+4)-y = 6[/tex]
Using distributive property: [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
[tex]y^2+4y-y=6[/tex]
Combine like terms;
[tex]y^2+3y = 6[/tex]
or
[tex]y^2+3y -6=0[/tex] which represents a quadratic equation.
B.
[tex]3a-7 = 2(7a-3)[/tex]
[tex]3a-7 = 14a-6[/tex]
or
[tex]11a+1 = 0[/tex] 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
[tex]4b^2 = 0[/tex] which represents the quadratic equation.
[2].
Given the parent function: [tex]y=x^2[/tex]
The reflection rule over x axis is given by;
[tex](x, y) \rightarrow (x, -y)[/tex]
then
the function become: [tex]y = -x^2[/tex]
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 [tex]y=-x^2-3[/tex] is the graph of [tex]y=-x^2[/tex] shifted 3 units down.
Therefore, the translation of the graph of [tex]y=x^2[/tex] to obtain [tex]y=-x^2-3[/tex] is, reflect over the x-axis and shift down 3
