Determine the Intersection Points of y=(-2x+4)(x+3) with the X-Axis

Q: Why do I set the whole function equal to zero?

X-intercepts occur where the graph crosses the x-axis, which means the y-coordinate is 0. So we set $ y = 0 $ to find these special x-values!

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

You'd need to factor the quadratic first or use the quadratic formula. The factored form $ y = (ax + b)(cx + d) $ makes finding x-intercepts much easier!

Q: How do I know which coordinate goes first?

Remember: (x, y) always! For x-intercepts, the y-coordinate is always 0, so you get points like $ (2, 0) $ and $ (-3, 0) $.

Q: Can a quadratic have more than 2 x-intercepts?

No! A quadratic function can have at most 2 x-intercepts. It could also have 1 (if it just touches the x-axis) or 0 (if it doesn't cross the x-axis at all).

Q: What does the zero product property actually mean?

If two numbers multiply to give zero, then at least one of them must be zero. It's impossible for two non-zero numbers to multiply and get zero!

Q: Do I need to expand the factored form first?

No! Keep it factored! The factored form $ (-2x + 4)(x + 3) = 0 $ makes it much easier to apply the zero product property directly.

Quadratic Functions with Factored Form

Determine the points of intersection of the function

$y=(-2x+4)(x+3)$

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 point with the X-axis

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

00:07 Substitute Y = 0 and solve for X values

00:13 Find what makes each factor zero in the multiplication

00:18 This is one solution

00:42 This is the second solution

00:48 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

$y=(-2x+4)(x+3)$

With the X

Step-by-step solution

To solve the problem, we need to find the x-intercepts of the quadratic function:

$y = (-2x + 4)(x + 3)$

The x-intercepts occur where the function equals zero, i.e., when $y = 0$ . Since the function is in factored form, we apply the zero-product property:

Set each factor equal to zero:
$(-2x + 4) = 0$
$x + 3 = 0$

Next, solve each equation for $x$ :

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

Subtract 4 from both sides: $-2x = -4$
Divide by -2: $x = 2$

For $x + 3 = 0$ :

Subtract 3 from both sides: $x = -3$

Therefore, the function intersects the x-axis at the points $(-3, 0)$ and $(2, 0)$ .

Additionally, when correlating with answer choices, choice 2 matches our derived solution:

$(-3, 0), (2, 0)$

Final Answer

$(-3,0),(2,0)$

Key Points to Remember

Essential concepts to master this topic

Zero Product Property: If AB = 0, then A = 0 or B = 0
Technique: Set each factor equal to zero: (-2x+4)=0 gives x=2
Check: Substitute back: y=(-2(2)+4)(2+3) = (0)(5) = 0 ✓

Common Mistakes

Avoid these frequent errors

Finding y-intercepts instead of x-intercepts
Don't substitute x=0 to find where the graph crosses the x-axis = gives you y-intercept (0,12) instead! This confuses axes and gives coordinate pairs with wrong positions. Always set y=0 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 I set the whole function equal to zero?

X-intercepts occur where the graph crosses the x-axis, which means the y-coordinate is 0. So we set $y = 0$ to find these special x-values!

What if the function wasn't already factored?

You'd need to factor the quadratic first or use the quadratic formula. The factored form $y = (ax + b)(cx + d)$ makes finding x-intercepts much easier!

How do I know which coordinate goes first?

Remember: (x, y) always! For x-intercepts, the y-coordinate is always 0, so you get points like $(2, 0)$ and $(-3, 0)$ .

Can a quadratic have more than 2 x-intercepts?

No! A quadratic function can have at most 2 x-intercepts. It could also have 1 (if it just touches the x-axis) or 0 (if it doesn't cross the x-axis at all).

What does the zero product property actually mean?

If two numbers multiply to give zero, then at least one of them must be zero. It's impossible for two non-zero numbers to multiply and get zero!

Do I need to expand the factored form first?

No! Keep it factored! The factored form $(-2x + 4)(x + 3) = 0$ makes it much easier to apply the zero product property directly.

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Determine the Intersection Points of y=(-2x+4)(x+3) with the X-Axis

Quadratic Functions with Factored 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 I set the whole function equal to zero?

What if the function wasn't already factored?

How do I know which coordinate goes first?

Can a quadratic have more than 2 x-intercepts?

What does the zero product property actually mean?

Do I need to expand the factored form first?

🌟 Unlock Your Math Potential

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