Finding X-Intercepts of the Quadratic: y = x(x + 5)

Q: Why do we set y = 0 to find x-intercepts?

X-intercepts are points where the graph crosses the x-axis. On the x-axis, the y-coordinate is always 0. So we set $ y = 0 $ to find where this happens!

Q: What if the quadratic wasn't already factored?

Great question! If you had $ y = x^2 + 5x $, you'd factor out the common x to get $ y = x(x + 5) $, then proceed the same way.

Q: How do I know which factor gives which x-intercept?

Set each factor equal to zero separately: x = 0 gives the intercept (0,0), and x + 5 = 0 gives x = -5, so the intercept (-5,0).

Q: Can a quadratic have more than two x-intercepts?

No! A quadratic function can have at most two x-intercepts. It might have exactly two (like this problem), one, or none at all.

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

They're the same x-values! X-intercepts are the points (x,0), while roots are just the x-values where the function equals zero. Here, the roots are x = 0 and x = -5.

X-Intercepts with Factored Quadratic Form

Determine the points of intersection of the function

$y=x(x+5)$

With the X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the intersection points with the X-axis

00:03 At the intersection points with the X-axis, the Y value must = 0

00:12 Substitute Y = 0 and solve for X values

00:16 Find what makes each factor in the product zero

00:20 This is one solution

00:23 This is the second solution

00:28 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

Determine the points of intersection of the function

$y=x(x+5)$

With the X

Step-by-step solution

To determine the points of intersection with the x-axis for the function $y = x(x+5)$ , follow these steps:

Step 1: Set the function equal to zero to find the x-intercepts: $y = 0$ .
Step 2: Solve the equation $x(x+5) = 0$ .

Considering the product $x(x+5) = 0$ :

If $x = 0$ , then one solution is $x = 0$ .
If $x+5 = 0$ , then solving for $x$ gives $x = -5$ .

Thus, the two points of intersection with the x-axis are:

$(-5, 0)$ and $(0, 0)$ .

Therefore, the points of intersection of the function $y = x(x+5)$ with the x-axis are $(-5, 0)$ and $(0, 0)$ .

Final Answer

$(-5,0),(0,0)$

Key Points to Remember

Essential concepts to master this topic

Zero Product Property: If a·b = 0, then a = 0 or b = 0
Technique: Set each factor equal to zero: x = 0 and x + 5 = 0
Check: Substitute back: 0(0+5) = 0 and (-5)(-5+5) = 0 ✓

Common Mistakes

Avoid these frequent errors

Setting y equal to the x-coordinate instead of zero
Don't set y = x to find x-intercepts = points like (5,5)! X-intercepts occur where the graph crosses the x-axis, meaning y = 0. Always set the entire function equal to zero when finding x-intercepts.

Practice Quiz

Test your knowledge with interactive questions

The following function has been graphed below:

$$ f(x)=-x^2+5x+6 $$

Calculate points A and B.

FAQ

Everything you need to know about this question

Why do we set y = 0 to find x-intercepts?

X-intercepts are points where the graph crosses the x-axis. On the x-axis, the y-coordinate is always 0. So we set $y = 0$ to find where this happens!

What if the quadratic wasn't already factored?

Great question! If you had $y = x^2 + 5x$ , you'd factor out the common x to get $y = x(x + 5)$ , then proceed the same way.

How do I know which factor gives which x-intercept?

Set each factor equal to zero separately: x = 0 gives the intercept (0,0), and x + 5 = 0 gives x = -5, so the intercept (-5,0).

Can a quadratic have more than two x-intercepts?

No! A quadratic function can have at most two x-intercepts. It might have exactly two (like this problem), one, or none at all.

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

They're the same x-values! X-intercepts are the points (x,0), while roots are just the x-values where the function equals zero. Here, the roots are x = 0 and x = -5.

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Finding X-Intercepts of the Quadratic: y = x(x + 5)

X-Intercepts with Factored Quadratic Form

❤️ 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 do we set y = 0 to find x-intercepts?

What if the quadratic wasn't already factored?

How do I know which factor gives which x-intercept?

Can a quadratic have more than two x-intercepts?

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

🌟 Unlock Your Math Potential

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