Question

• Parent Function: y=x^2=• Using the Vertex Form: y = a (x - h)^2 +K• Predict the vertex (h, k)• Determine the orientation• Is there a vertical shift? If so, describe the transformation.• Is there a horizontal shift? If so, describe thetransformation.1. y = x^2 + 5

Answer 1

Step-by-step explanation

Step 1

parent function:

`y=x^2`

and the transformed function is

`y=x^2+5`

hence ,

`y=x^2\rightarrow y=x^2+5`

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:

`\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}`

therefore, the vertex is

`\begin{gathered} \text{vertex ( h,k)} \\ \text{vertex ( 0,5)} \end{gathered}`

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

`\begin{gathered} y=x^2+5 \\ a=1>0,\text{ hence} \end{gathered}`

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