The function g(x) is a transformation of the quadratic parent function, A(x) = X2. What function is g(x)?

Q1) g(x)=2x^2-10g(x)=2x

2

−10

Q2) g(x)=6x^2-1g(x)=6x

2

−1

Q3) A. g(x)=x^2+2g(x)=x

2

+2

Step-by-step explanation:

Q1) being f(x)=2x^2-8f(x)=2x

2

−8 and g(x) is the same function but translated 2 units down, that is:

\begin{gathered}g(x)=f(x)-2\\g(x)=2x^2-8-2\\g(x)=2x^2-10\end{gathered}

g(x)=f(x)−2

g(x)=2x

2

−8−2

g(x)=2x

2

−10

Q2) f(x)=\frac{3}{4}x^2-1f(x)=

4

3

x

2

−1 and f(x) has a vertical stretch, the vertical strech is given by multiplying the X factor for the stretch:

\begin{gathered}g(x)=8*\frac{3}{4}x^2-1g(x)=6x^2-1\end{gathered}

g(x)=8∗

4

3

x

2

−1

g(x)=6x

2

−1

Q3) Looking at the graph we can notice that thhe function g(x) is the same fuction f(x) but it has been displaced 2 units up, so:

\begin{gathered}g(x)=f(x)+2\\g(x)=x^2+2\end{gathered}

g(x)=f(x)+2

g(x)=x

2

+2

The correct answer is A.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions