Transforming y = x²: Shifting 4 Right and 3 Up

Q: Why is it (x-4) when moving right, not (x+4)?

This is the most confusing part! Think of it this way: to get the same y-value as before, x must be 4 units bigger. So when x=4, we get (4-4)² = 0², which is like the original function at x=0.

Q: How do I remember which direction horizontal shifts go?

Use this memory trick: "Opposite Day" for horizontal shifts! Right means subtract, left means add. Vertical shifts are normal: up means add, down means subtract.

Q: Can I do the shifts in any order?

Yes! You can apply horizontal and vertical shifts in any order - the final result will be the same. Most people find it easier to do horizontal first, then vertical.

Q: How do I check if my transformed function is correct?

Pick a simple point! For $ y=(x-4)^2+3 $, try x=4: you get y=3. This means the vertex moved from (0,0) to (4,3), which matches 4 right and 3 up!

Q: What if I need to move left or down instead?

Left h units: use (x+h)Down k units: subtract kExample: 2 left, 5 down gives $ y=(x+2)^2-5 $

Function Transformations with Horizontal and Vertical Shifts

Which equation represents the function

$y=x^2$

moved 4 spaces to the right

and 3 spaces upwards?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which equation represents the function

$y=x^2$

moved 4 spaces to the right

and 3 spaces upwards?

Step-by-step solution

To solve this problem, we will apply transformations to the function $y = x^2$ .

Step 1: Horizontal Shift
When a function is moved 4 units to the right, the $x$ value inside the function is replaced with $x - 4$ . So, the transformation of $y = x^2$ becomes $y = (x - 4)^2$ .

Step 2: Vertical Shift
When a function is moved 3 units upwards, we add 3 to the whole function. Applying this to our function from Step 1 gives us $y = (x - 4)^2 + 3$ .

Therefore, after the required transformations, the equation representing the function moved 4 units to the right and 3 units upwards is $y = (x - 4)^2 + 3$ .

Checking the multiple-choice options, the correct choice is:

$y=(x-4)^2+3$

Final Answer

$y=(x-4)^2+3$

Key Points to Remember

Essential concepts to master this topic

Horizontal Rule: Moving right h units means replace x with (x - h)
Vertical Technique: Moving up k units adds k: $y = f(x) + k$
Check: Substitute test point: (4,3) into $y=(x-4)^2+3$ gives y=3 ✓

Common Mistakes

Avoid these frequent errors

Confusing horizontal shift direction
Don't use (x+4) when moving right = moves left instead! Students think "right means plus" but horizontal shifts are opposite to the sign. Always remember: right h units means (x-h), left h units means (x+h).

Practice Quiz

Test your knowledge with interactive questions

Find the corresponding algebraic representation of the drawing:

FAQ

Everything you need to know about this question

Why is it (x-4) when moving right, not (x+4)?

This is the most confusing part! Think of it this way: to get the same y-value as before, x must be 4 units bigger. So when x=4, we get (4-4)² = 0², which is like the original function at x=0.

How do I remember which direction horizontal shifts go?

Use this memory trick: "Opposite Day" for horizontal shifts! Right means subtract, left means add. Vertical shifts are normal: up means add, down means subtract.

Can I do the shifts in any order?

Yes! You can apply horizontal and vertical shifts in any order - the final result will be the same. Most people find it easier to do horizontal first, then vertical.

How do I check if my transformed function is correct?

Pick a simple point! For $y=(x-4)^2+3$ , try x=4: you get y=3. This means the vertex moved from (0,0) to (4,3), which matches 4 right and 3 up!

What if I need to move left or down instead?

Left h units: use (x+h)
Down k units: subtract k
Example: 2 left, 5 down gives $y=(x+2)^2-5$

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parabola Families questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime