GOZUNTA
Try it now
All courses Algebra I · F-BF.3 62 of 76
Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.

Interpret \(f(x)+k\) as a vertical shift of a quadratic or absolute-value function

Problem
Identify the vertical shift from parent function \(f(x)=x^2\) to transformed function \(g(x)=x^2+5\).
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Choose exactly what to practice.

Browse the learning objectives and included problem types, then build a session around the math you want to work on.

Create a free account
With paid access

Give your progress record more evidence.

A larger problem bank gives you more chances to see whether a skill is becoming dependable.

Compare plans

Hint

Compare \(g(x)=x^2+5\) to the parent \(f(x)=x^2\) and focus on the \(+5\) outside the square.

Adding a positive number outside the function shifts the graph up by that amount.

Solution walkthrough

01

Compare the two rules

\[\begin{aligned} f(x)=x^2 \\ g(x)=x^2+5=f(x)+5 \end{aligned}\]

The transformed rule adds 5 outside the parent function's output. The input expression itself is unchanged.

02

Interpret an outside addition

\[g(x)=f(x)+5~->~\text{every}~\text{output}~\text{increases}~by~5\]

Adding a constant after function evaluation changes y-values while preserving x-values, so it is a vertical transformation.

03

Determine direction and distance

\[+5~->~\text{up}~5~\text{units}\]

Every point (x,y) on the parent becomes (x,y+5), moving upward by 5 units.

04

Check a landmark

\[\text{parent}~\text{vertex}~(0,0)~->~\text{new}~\text{vertex}~(0,5)\]

The inspected answer graph shows the parent and transformed vertices separated vertically by 5, confirming the shift.

+

Another way

  1. Evaluate both at x=0: f(0)=0 and g(0)=5, while their shapes and x-locations match.

!

Common mistake

Do not call the outside +5 a horizontal shift. Horizontal shifts change the input inside the function; this constant changes outputs.

Answer graph showing the exact transformed function and the requested shift, scale, reflection, comparison, or contextual feature.
shift: up 5

Solution walkthrough video