Finding X-Axis Intersections: Zero Substitution Method

Q: Why do we set y = 0 instead of x = 0 for x-intercepts?

At x-intercepts, the curve crosses the x-axis where the height is zero. This means y = 0! Setting x = 0 would find where the curve crosses the y-axis instead.

Q: What's the difference between x-intercepts and y-intercepts?

X-intercepts: Points where the graph crosses the x-axis (set y = 0)Y-intercepts: Points where the graph crosses the y-axis (set x = 0)

Q: For y = (x - p)², why is the x-intercept at x = p?

When we set y = 0, we get $ (x - p)^2 = 0 $. Since any number squared equals zero only when that number is zero, we have $ x - p = 0 $, so $ x = p $.

Q: How can I remember which variable to set to zero?

Think about the axis name! For x-intercepts, the y-coordinate is zero. For y-intercepts, the x-coordinate is zero. The variable that's NOT in the name gets set to zero!

Q: What if I accidentally use x = 0 instead of y = 0?

You'll get the wrong intersection point! For $ y = (x - p)^2 $, substituting x = 0 gives y = p², which is the y-intercept at (0, p²), not the x-intercept.

X-Axis Intercepts with Substitution Confusion

To work out the points of intersection with the X axis, you must substitute $x=0$ .

❤️ 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 To find the intersection point with the X-axis, we substitute X = 0?

00:03 Let's draw a parabola that has intersection points with the X-axis

00:12 This is the line where X = 0 (Y-axis)

00:16 At the intersection points with the X-axis on the graph, we can see they are not 0

00:22 At the intersection points with the X-axis - Y = 0

00:26 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

To work out the points of intersection with the X axis, you must substitute $x=0$ .

Step-by-step solution

To solve this problem, we need to determine whether substituting $x = 0$ gives us the points of intersection with the x-axis for the parabola $y = (x - p)^2$ .

To find the x-intercepts of any function, we set $y = 0$ because the x-intercepts occur where the curve meets the x-axis, which implies a zero output or function value:

Start with the equation: $y = (x - p)^2$ .
Set $y = 0$ for the x-intercept: $(x - p)^2 = 0$ .
Solving this gives $(x - p) = 0$ , which simplifies to $x = p$ .
Thus, the x-intercept happens at the point where $x = p$ , not where $x = 0$ .

Therefore, substituting $x = 0$ does not provide the x-intercepts. Instead, it provides the y-intercept. Therefore, the statement given in the problem is False.

Thus, the solution to the problem is False.

Final Answer

False

Key Points to Remember

Essential concepts to master this topic

Rule: Set y = 0 to find x-intercepts, not x = 0
Technique: Solve $(x - p)^2 = 0$ gives x = p
Check: Verify x-intercept gives y = 0 when substituted back ✓

Common Mistakes

Avoid these frequent errors

Substituting x = 0 to find x-intercepts
Don't substitute x = 0 to find x-intercepts = this gives you the y-intercept instead! Setting x = 0 finds where the curve crosses the y-axis, not the x-axis. Always set y = 0 to find x-intercepts.

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 do we set y = 0 instead of x = 0 for x-intercepts?

At x-intercepts, the curve crosses the x-axis where the height is zero. This means y = 0! Setting x = 0 would find where the curve crosses the y-axis instead.

What's the difference between x-intercepts and y-intercepts?

X-intercepts: Points where the graph crosses the x-axis (set y = 0)

Y-intercepts: Points where the graph crosses the y-axis (set x = 0)

For y = (x - p)², why is the x-intercept at x = p?

When we set y = 0, we get $(x - p)^2 = 0$ . Since any number squared equals zero only when that number is zero, we have $x - p = 0$ , so $x = p$ .

How can I remember which variable to set to zero?

Think about the axis name! For x-intercepts, the y-coordinate is zero. For y-intercepts, the x-coordinate is zero. The variable that's NOT in the name gets set to zero!

What if I accidentally use x = 0 instead of y = 0?

You'll get the wrong intersection point! For $y = (x - p)^2$ , substituting x = 0 gives y = p², which is the y-intercept at (0, p²), not the x-intercept.

🌟 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