Find X-Axis Intersections of y=(x+3)² : Quadratic Function Analysis

Q: Why is there only one x-intercept instead of two?

Great observation! Most quadratics have two x-intercepts, but $ y = (x+3)^2 $ is special. It touches the x-axis at exactly one point: $ (-3, 0) $. This is called a double root because the parabola just touches the axis without crossing it.

Q: How do I know when to set y = 0?

Always set y = 0 when finding x-intercepts! The x-axis is where y-coordinates equal zero. Think of it this way: "Where does my graph touch the ground (y = 0)?"

Q: What if I get confused about the sign?

Remember: $ (x+3)^2 = 0 $ means x + 3 = 0, so x = -3. The intercept is at $ (-3, 0) $, not $ (3, 0) $! Always solve the equation inside the parentheses.

Q: Can I check my answer another way?

Yes! Graph the function or use a table of values. You'll see that when x = -3, y = 0, confirming your intercept. You can also substitute: $ y = (-3+3)^2 = 0^2 = 0 $ ✓

Q: Why are the other answer choices wrong?

$ (3, 0) $ comes from the wrong sign. $ (0, 3) $ and $ (0, -3) $ are y-intercepts (where x = 0), not x-intercepts. Always check which axis you're finding intersections with!

X-Axis Intersections with Perfect Square Quadratics

Find the intersection of the function

$y=(x+3)^2$

With the X

❤️ 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

00:00 Find the intersection point of the function with the X-axis

00:03 At the intersection point with the X-axis Y =0

00:07 Therefore, we substitute Y =0 and solve to find the intersection point with the X-axis

00:11 Extract the root to eliminate the power

00:24 Isolate X

00:31 This is the X value at the intersection point, we substitute Y=0 as we stated at the point

00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the intersection of the function

$y=(x+3)^2$

With the X

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Identify the function as $y = (x+3)^2$ .
Step 2: Set $y = 0$ to find the intersection with the x-axis.
Step 3: Solve $(x+3)^2 = 0$ to find the x-coordinate.

Let's proceed through each step:
Step 1: We are given the function $y = (x+3)^2$ .
Step 2: To find where this function intersects the x-axis, set $y = 0$ :

$(x+3)^2 = 0$

Step 3: Solve the equation:
The equation $(x+3)^2 = 0$ suggests that $x+3 = 0$ ,
which simplifies to $x = -3$ .

Therefore, the intersection point is where $x = -3$ and $y = 0$ , giving us the intersection at $(-3, 0)$ .

Thus, the solution to the problem is $(-3, 0)$ , corresponding to choice given as $(-3, 0)$ .

Final Answer

$(-3,0)$

Key Points to Remember

Essential concepts to master this topic

X-Intercepts: Set y = 0 to find where function crosses x-axis
Perfect Square: $(x+3)^2 = 0$ means x + 3 = 0, so x = -3
Verify: Substitute x = -3: $y = (-3+3)^2 = 0^2 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Expanding the perfect square unnecessarily
Don't expand $(x+3)^2$ to $x^2 + 6x + 9 = 0$ then use quadratic formula = harder work for same answer! Perfect squares already show the solution directly. Always recognize $(x+a)^2 = 0$ means x = -a immediately.

Practice Quiz

Test your knowledge with interactive questions

Find the intersection of the function

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

With the Y

FAQ

Everything you need to know about this question

Why is there only one x-intercept instead of two?

Great observation! Most quadratics have two x-intercepts, but $y = (x+3)^2$ is special. It touches the x-axis at exactly one point: $(-3, 0)$ . This is called a double root because the parabola just touches the axis without crossing it.

How do I know when to set y = 0?

Always set y = 0 when finding x-intercepts! The x-axis is where y-coordinates equal zero. Think of it this way: "Where does my graph touch the ground (y = 0)?"

What if I get confused about the sign?

Remember: $(x+3)^2 = 0$ means x + 3 = 0, so x = -3. The intercept is at $(-3, 0)$ , not $(3, 0)$ ! Always solve the equation inside the parentheses.

Can I check my answer another way?

Yes! Graph the function or use a table of values. You'll see that when x = -3, y = 0, confirming your intercept. You can also substitute: $y = (-3+3)^2 = 0^2 = 0$ ✓

Why are the other answer choices wrong?

$(3, 0)$ comes from the wrong sign. $(0, 3)$ and $(0, -3)$ are y-intercepts (where x = 0), not x-intercepts. Always check which axis you're finding intersections with!

🌟 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

Find X-Axis Intersections of y=(x+3)² : Quadratic Function Analysis

X-Axis Intersections with Perfect Square Quadratics

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is there only one x-intercept instead of two?

How do I know when to set y = 0?

What if I get confused about the sign?

Can I check my answer another way?

Why are the other answer choices wrong?

🌟 Unlock Your Math Potential

More Questions

Parabola of the Form y=(x-p)²

Solve (x-5)² = 0: Finding X-Axis Intersections of a Quadratic Function

Finding X-Intercepts of y=(x-1/2)²: Quadratic Function Analysis

Find X-Intercepts of y=(x-2)² : Quadratic Function Analysis

Find Y-Intercept of y=(x-5)²: Quadratic Function Analysis