Determine Intersection Points of y = (x + 8)(x - 9) on the X-Axis

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

You'd need to factor the quadratic first or use other methods like the quadratic formula. The factored form $ (x + 8)(x - 9) $ makes finding zeros much easier!

Q: How do I remember which sign goes with which intercept?

Look at the factors: x + 8 = 0 gives x = -8, and x - 9 = 0 gives x = 9. The sign in the factor is opposite to the x-intercept value.

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

No, a quadratic function can have at most 2 x-intercepts. It might have 2 (like this problem), 1 (if it just touches the x-axis), or 0 (if it doesn't cross the x-axis at all).

Quadratic Functions with Factored Form Intercepts

Determine the points of intersection of the function

$y=(x+8)(x-9)$

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 this point, the Y value is zero.

00:16 So, we set Y to zero and solve for X.

00:22 Find out which factors make the equation zero.

00:26 Great job! This is one solution.

00:38 Here's the second solution.

00:44 And that's how we solve 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

$y=(x+8)(x-9)$

With the X

Step-by-step solution

The solution to the problem involves finding the x-intercepts of the given quadratic function, which are the points where the function intersects the x-axis (i.e., where $y = 0$ ).

Step by step solution:

Set the function equal to zero: $(x+8)(x-9) = 0$ .
The product of two terms is zero if and only if at least one of the terms is zero. Therefore, we solve:
$x+8 = 0$ or $x-9 = 0$ .
For $x+8 = 0$ :
Subtract 8 from both sides to isolate $x$ :
$x = -8$ .
For $x-9 = 0$ :
Add 9 to both sides to isolate $x$ :
$x = 9$ .

The function intersects the x-axis at the points $(-8, 0)$ and $(9, 0)$ .

Therefore, the points of intersection of the function with the x-axis are $(-8, 0)$ and $(9, 0)$ .

Final Answer

$(-8,0),(9,0)$

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 + 8 = 0 gives x = -8
Check: Substitute back: (-8 + 8)(-8 - 9) = 0(-17) = 0 ✓

Common Mistakes

Avoid these frequent errors

Solving factors without setting them equal to zero
Don't just solve x + 8 and x - 9 directly = meaningless results! You need y = 0 for x-intercepts, so the entire expression (x + 8)(x - 9) must equal zero first. Always set the factored expression equal to zero, then solve each factor separately.

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 I set the equation equal to zero to find x-intercepts?

X-intercepts occur where the graph crosses the x-axis, which means y = 0. So we need to find all x-values that make our function equal zero!

What if the function wasn't already factored?

You'd need to factor the quadratic first or use other methods like the quadratic formula. The factored form $(x + 8)(x - 9)$ makes finding zeros much easier!

How do I remember which sign goes with which intercept?

Look at the factors: x + 8 = 0 gives x = -8, and x - 9 = 0 gives x = 9. The sign in the factor is opposite to the x-intercept value.

Are the y-coordinates always zero for x-intercepts?

Yes! By definition, x-intercepts are points where the graph crosses the x-axis, so the y-coordinate is always zero. That's why our answers are (-8, 0) and (9, 0).

Can a quadratic have more than two x-intercepts?

No, a quadratic function can have at most 2 x-intercepts. It might have 2 (like this problem), 1 (if it just touches the x-axis), or 0 (if it doesn't cross the x-axis at all).

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Determine Intersection Points of y = (x + 8)(x - 9) on the X-Axis

Quadratic Functions with Factored Form Intercepts

❤️ 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 I set the equation equal to zero to find x-intercepts?

What if the function wasn't already factored?

How do I remember which sign goes with which intercept?

Are the y-coordinates always zero for x-intercepts?

Can a quadratic have more than two x-intercepts?

🌟 Unlock Your Math Potential

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