Find Intersection Points of the Quadratic: y=(-x-3)(x-1) with the X-axis

Q: Why do x-intercepts always have y = 0?

X-intercepts are the points where the graph crosses the x-axis. Since the x-axis is the line where y = 0, all points on it have a y-coordinate of zero!

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

You'll need to factor it first or use other methods like the quadratic formula. The zero product property only works when the equation is in factored form.

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 never crosses the x-axis).

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

Set each factor equal to zero separately: $ -x-3=0 $ becomes $ x=-3 $, and $ x-1=0 $ becomes $ x=1 $. Each factor gives one solution!

Q: What does the negative sign in front mean?

The negative sign in $ (-x-3) $ affects the entire factor. When solving $ -x-3=0 $, you get $ -x=3 $, so $ x=-3 $.

X-intercepts with Factored Quadratics

Determine the points of intersection of the function

$y=(-x-3)(x-1)$

With the X

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find where the graph crosses the X-axis.

00:14 At this point, the Y value is zero.

00:17 So, we substitute Y equals zero, and solve for X.

00:23 Find out which values of X make each factor zero.

00:28 Here's one solution, when X equals this value.

00:38 And here's the second solution, for this X value.

00:42 That's how we solve this equation!

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

$y=(-x-3)(x-1)$

With the X

Step-by-step solution

To solve for the x-intercepts of the function $y = (-x-3)(x-1)$ , we need to find where $y = 0$ .

The equation becomes:

$(-x-3)(x-1) = 0$

This equation is satisfied if either of the factors equals zero:

Set the first factor to zero: $-x - 3 = 0$ .
Solve for $x$ : $-x = 3$ , therefore $x = -3$ .
Set the second factor to zero: $x - 1 = 0$ .
Solve for $x$ : $x = 1$ .

Thus, the x-intercepts are $(-3, 0)$ and $(1, 0)$ .

These correspond with option 3 from the list of choices.

Therefore, the points of intersection of the function with the x-axis are $(1,0),(-3,0)$ .

Final Answer

$(1,0),(-3,0)$

Key Points to Remember

Essential concepts to master this topic

Zero Product Property: If $ab = 0$ , then $a = 0$ or $b = 0$
Set Each Factor to Zero: $-x-3=0$ gives $x=-3$ and $x-1=0$ gives $x=1$
Check Y-coordinates: X-intercepts always have y-coordinate of 0, giving points (-3,0) and (1,0) ✓

Common Mistakes

Avoid these frequent errors

Writing y-coordinates as non-zero values
Don't write the x-intercepts as (-3,1) or (1,-3) = wrong points! X-intercepts are where the graph crosses the x-axis, so y must equal zero. Always write x-intercepts as (x,0) with zero as the second coordinate.

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 x-intercepts always have y = 0?

X-intercepts are the points where the graph crosses the x-axis. Since the x-axis is the line where y = 0, all points on it have a y-coordinate of zero!

What if the quadratic isn't already factored?

You'll need to factor it first or use other methods like the quadratic formula. The zero product property only works when the equation is in factored form.

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 never crosses the x-axis).

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

Set each factor equal to zero separately: $-x-3=0$ becomes $x=-3$ , and $x-1=0$ becomes $x=1$ . Each factor gives one solution!

What does the negative sign in front mean?

The negative sign in $(-x-3)$ affects the entire factor. When solving $-x-3=0$ , you get $-x=3$ , so $x=-3$ .

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Find Intersection Points of the Quadratic: y=(-x-3)(x-1) with the X-axis

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 x-intercepts always have y = 0?

What if the quadratic isn't already factored?

Can a quadratic have more than 2 x-intercepts?

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

What does the negative sign in front mean?

🌟 Unlock Your Math Potential

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