Determine Intersection Points for y = (x - 11)(x + 1)

Q: Why do we set the function equal to zero?

X-intercepts occur where the graph crosses the x-axis. On the x-axis, the y-coordinate is always zero, so we need $ y = 0 $.

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

You'd need to factor the quadratic first! For example, $ x^2 - 10x - 11 = 0 $ factors to $ (x - 11)(x + 1) = 0 $, then solve the same way.

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

No! A quadratic function can have at most two x-intercepts. It could also have one (touching the x-axis) or none (not crossing the x-axis).

Q: How do I remember which coordinates go where?

Remember: x-intercepts have the form (x-value, 0). The y-coordinate is always zero because you're on the x-axis!

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

They're the same thing! Roots, zeros, x-intercepts, and solutions all refer to the x-values where $ y = 0 $.

X-intercepts with Factored Quadratic Functions

Determine the points of intersection of the function

$y=(x-11)(x+1)$

With the X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find where the graph crosses the X-axis.

00:13 At these points, the Y value is zero.

00:17 So, we set Y to zero and solve for X.

00:22 Look at each factor to see what makes them zero.

00:28 Here, we have one solution for X.

00:37 And here is another solution for X.

00:45 That's how we find the solution to the problem!

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

$y=(x-11)(x+1)$

With the X

Step-by-step solution

To determine the points where the function intersects the x-axis, we need to find the x-intercepts. These occur where $y = 0$ .

The function is given as $y = (x-11)(x+1)$ . To find the x-intercepts, we set this function equal to zero:

$(x-11)(x+1) = 0$ .

This equation implies that the product is zero when either $x-11 = 0$ or $x+1 = 0$ .

Solving these equations, we find:

$x-11 = 0$ leads to $x = 11$ .
$x+1 = 0$ leads to $x = -1$ .

Thus, the points of intersection with the x-axis are $(-1, 0)$ and $(11, 0)$ .

Therefore, the solution to the problem is $(-1, 0), (11, 0)$ .

Final Answer

$(-1,0),(11,0)$

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 - 11 = 0 and x + 1 = 0
Check: Substitute back: (-1 - 11)(-1 + 1) = (-12)(0) = 0 ✓

Common Mistakes

Avoid these frequent errors

Setting the entire expression equal to the x-value instead of zero
Don't set (x - 11)(x + 1) = x to find intersections = wrong equation! This finds where the parabola equals the line y = x, not the x-axis. Always set the 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 the function equal to zero?

X-intercepts occur where the graph crosses the x-axis. On the x-axis, the y-coordinate is always zero, so we need $y = 0$ .

What if the function wasn't already factored?

You'd need to factor the quadratic first! For example, $x^2 - 10x - 11 = 0$ factors to $(x - 11)(x + 1) = 0$ , then solve the same way.

Can a quadratic have more than two x-intercepts?

No! A quadratic function can have at most two x-intercepts. It could also have one (touching the x-axis) or none (not crossing the x-axis).

How do I remember which coordinates go where?

Remember: x-intercepts have the form (x-value, 0). The y-coordinate is always zero because you're on the x-axis!

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

They're the same thing! Roots, zeros, x-intercepts, and solutions all refer to the x-values where $y = 0$ .

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Determine Intersection Points for y = (x - 11)(x + 1)

X-intercepts with Factored Quadratic Functions

❤️ 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 the function equal to zero?

What if the function wasn't already factored?

Can a quadratic have more than two x-intercepts?

How do I remember which coordinates go where?

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

🌟 Unlock Your Math Potential

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