Find y = -x² Transformed: 3 Units Left and 4 Units Up

Q: How do I remember which transformation goes where?

Use this trick: Horizontal changes go INSIDE with the x, vertical changes go OUTSIDE. So (x+3) affects horizontal position, +4 affects vertical position.

Q: How can I verify my answer is correct?

Check the vertex location! The original vertex at (0,0) should move to (-3,4). In $ y = -(x+3)^2 + 4 $, when x = -3, you get y = 4. Perfect match!

Q: What's the difference between the four answer choices?

Choice 1: -(x+3)² + 4 ✓ (correct: negative parabola, shifted left and up)Choice 2: (x+3)² + 4 (wrong: opens upward instead of downward)Choice 3: (x+3)² - 4 (wrong: opens up AND moves down)Choice 4: -(x+3)² - 4 (wrong: moves down instead of up)

Function Transformations with Horizontal and Vertical Shifts

Choose the equation that represents the function

$y=-x^2$

moved 3 spaces to the left

and 4 spaces up.

❤️ 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

Choose the equation that represents the function

$y=-x^2$

moved 3 spaces to the left

and 4 spaces up.

Step-by-step solution

To solve this problem, the following steps are necessary:

We begin with the original function:

$y = -x^2$

First, we apply the horizontal shift of 3 units to the left. Moving a graph left involves adding a number to $x$ in the equation. Hence, replace $x$ with $(x + 3)$ . This manipulatively affects the original function:

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

Next, we apply the vertical shift of 4 units upward. This involves adding 4 to the function:

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

Therefore, the equation representing the parabola moved 3 spaces to the left and 4 spaces up is:

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

Verification against the choices confirms that the correct answer is choice (1):

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

This is indeed the equation that results after applying the given transformations to the original function $y = -x^2$ .

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Horizontal Shifts: Moving left means adding inside parentheses (x+3)
Vertical Shifts: Moving up means adding to entire function: +4
Check: Vertex moved from (0,0) to (-3,4) matches transformations ✓

Common Mistakes

Avoid these frequent errors

Confusing horizontal shift directions
Don't think moving left means subtracting = y = -(x-3)² + 4! This actually moves the graph RIGHT 3 units. Always remember: left means ADD inside parentheses, right means SUBTRACT.

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 does moving left mean adding to x?

This seems backwards but think about it: when x = -3, the expression (x+3) equals zero! So the vertex occurs at x = -3, which is 3 units left of the original.

How do I remember which transformation goes where?

Use this trick: Horizontal changes go INSIDE with the x, vertical changes go OUTSIDE. So (x+3) affects horizontal position, +4 affects vertical position.

What if the coefficient of x² was positive instead of negative?

The transformations work exactly the same way! Whether it's $y = x^2$ or $y = -x^2$ , moving left 3 and up 4 gives you (x+3)² + 4 or -(x+3)² + 4.

How can I verify my answer is correct?

Check the vertex location! The original vertex at (0,0) should move to (-3,4). In $y = -(x+3)^2 + 4$ , when x = -3, you get y = 4. Perfect match!

What's the difference between the four answer choices?

Choice 1: -(x+3)² + 4 ✓ (correct: negative parabola, shifted left and up)
Choice 2: (x+3)² + 4 (wrong: opens upward instead of downward)
Choice 3: (x+3)² - 4 (wrong: opens up AND moves down)
Choice 4: -(x+3)² - 4 (wrong: moves down instead of up)

🌟 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