Calculate Intersection Points of Quadratic y = (x-2)(x+4)

Q: Why do I set the equation equal to zero?

X-intercepts are where the graph crosses the x-axis. On the x-axis, all y-values equal zero, so we set $ y = 0 $ to find these crossing points.

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

You'd need to factor it first or use other methods like the quadratic formula. Since $ y = (x-2)(x+4) $ is already factored, we can directly apply the Zero Product Property!

Q: How do I remember which x-value goes with each factor?

For $ (x-2) = 0 $, add 2 to get $ x = 2 $. For $ (x+4) = 0 $, subtract 4 to get $ x = -4 $. Do the opposite of what's inside the parentheses!

Q: Why are both y-coordinates zero in the answer?

X-intercepts always have y-coordinates of zero because they're points where the graph touches the x-axis. The format is always $ (x, 0) $ for x-intercepts.

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), exactly one (if it just touches the x-axis), or none (if it doesn't cross the x-axis at all).

X-intercepts with Factored Quadratics

Determine the points of intersection of the function

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

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 with the X-axis, the Y value must = 0

00:07 Substitute Y = 0 and solve to find X values

00:13 Find what zeros each factor in the product

00:16 This is one solution

00:28 This is the second solution

00:37 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

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

With the X

Step-by-step solution

To solve this problem, we will find the x-intercepts of the function $y = (x-2)(x+4)$ .

The function is already in factored form: $y = (x-2)(x+4)$ . The x-intercepts occur where $y = 0$ .

Set the equation equal to zero:

$(x-2)(x+4) = 0$

Using the Zero Product Property, each factor must equal zero:

First solve $x - 2 = 0$ :

Add 2 to both sides: $x = 2$

Next, solve $x + 4 = 0$ :

Subtract 4 from both sides: $x = -4$

The x-intercepts of the function are at points $(2, 0)$ and $(-4, 0)$ .

Thus, the points at which the function intersects the x-axis are $(-4,0)$ and $(2,0)$ .

Therefore, the correct answer is choice 3: $(-4,0),(2,0)$ .

Final Answer

$(-4,0),(2,0)$

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 - 2 = 0 and x + 4 = 0
Check: Substitute back: (2-2)(2+4) = 0(6) = 0 and (-4-2)(-4+4) = (-6)(0) = 0 ✓

Common Mistakes

Avoid these frequent errors

Confusing x-intercepts with y-intercepts
Don't find where x = 0 to get y-intercepts = points like (0, -8)! X-intercepts occur where y = 0, giving coordinates with zero y-values. Always set y = 0 to find 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 I set the equation equal to zero?

X-intercepts are where the graph crosses the x-axis. On the x-axis, all y-values equal zero, so we set $y = 0$ to find these crossing points.

What if the quadratic isn't already factored?

You'd need to factor it first or use other methods like the quadratic formula. Since $y = (x-2)(x+4)$ is already factored, we can directly apply the Zero Product Property!

How do I remember which x-value goes with each factor?

For $(x-2) = 0$ , add 2 to get $x = 2$ . For $(x+4) = 0$ , subtract 4 to get $x = -4$ . Do the opposite of what's inside the parentheses!

Why are both y-coordinates zero in the answer?

X-intercepts always have y-coordinates of zero because they're points where the graph touches the x-axis. The format is always $(x, 0)$ for x-intercepts.

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), exactly one (if it just touches the x-axis), or none (if it doesn't cross the x-axis at all).

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Calculate Intersection Points of Quadratic y = (x-2)(x+4)

X-intercepts with Factored 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 do I set the equation equal to zero?

What if the quadratic isn't already factored?

How do I remember which x-value goes with each factor?

Why are both y-coordinates zero in the answer?

Can a quadratic have more than two x-intercepts?

🌟 Unlock Your Math Potential

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