Respuesta :
Explanation
Step 1
parent function:
[tex]y=x^2[/tex]and the transformed function is
[tex]y=x^2+5[/tex]hence ,
[tex]y=x^2\rightarrow y=x^2+5[/tex]we can see that 5 was added to the parent function to get the actual function, so
transformation : 5 was added
: To move a function up, you add outside the function: f (x) + b is f (x) moved up b units
so we can conclude:
the function was shifted 5 units up
Step 2
get the vertex form:
[tex]\begin{gathered} y=x^2+5 \\ y=x^2+5\rightarrow y=(a-x)^2+h \\ \text{hence} \\ (a-x)=x \\ a=0 \\ \text{and} \\ h=5 \end{gathered}[/tex]therefore, the vertex is
[tex]\begin{gathered} \text{vertex ( h,k)} \\ \text{vertex ( 0,5)} \end{gathered}[/tex]Step 3
orientation :
The orientation of a quadratic function is determined solely by the coefficient ax^2+bx+c=0. If this coefficient is positive, the parabola opens up. If this coefficient is negative, the parabola opens down
so, let's check
[tex]\begin{gathered} y=x^2+5 \\ a=1>0,\text{ hence} \end{gathered}[/tex]the parabola opens up
Step 3
horizontal shift:
Given a function f, a new function g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right. If h is negative, the graph will shift left.
we can see that in the argument nothing was added, so
there is not horizontal shift
I hope this helps you
