Finding Intersection Points: Solve for x in y = (x-1)(x+10)

Q: Why do we set y = 0 to find x-intercepts?

X-intercepts are points where the graph crosses the x-axis. At these points, the y-coordinate is always 0! So we set the function equal to zero to find where it touches the x-axis.

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

You'll need to factor it first or use the quadratic formula. Factored form like $ y = (x-1)(x+10) $ makes finding x-intercepts much easier using the Zero Product Property.

Q: How do I remember which sign to use when solving?

Think of it as undoing the operation! For $ (x-1) = 0 $, add 1 to both sides. For $ (x+10) = 0 $, subtract 10 from both sides.

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

No! A quadratic function can have at most 2 x-intercepts. It might have 2 (like this problem), 1 (touches x-axis), or 0 (doesn't cross x-axis).

X-Intercepts with Factored Quadratics

Determine the points of intersection of the function

$y=(x-1)(x+10)$

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 X-axis, Y value must = 0

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

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

00:20 This is one solution

00:28 This is second solution

00:33 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

$y=(x-1)(x+10)$

With the X

Step-by-step solution

To find where the function intersects the x-axis, we set $y = (x - 1)(x + 10) = 0$ .

Using the Zero Product Property, if the product equals zero, at least one of the factors must be zero:

If $(x - 1) = 0$ , then $x = 1$ .
If $(x + 10) = 0$ , then $x = -10$ .

Thus, the function intersects the x-axis at the points where $x = 1$ and $x = -10$ . These give us the points $(1, 0)$ and $(-10, 0)$ respectively, as the y-coordinate is zero for all x-intercepts.

Therefore, the points of intersection are $(1, 0)$ and $-10, 0)$ .

Final Answer

$(1,0),(-10,0)$

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: (x-1) = 0 gives x = 1
Check: Substitute x-values back: (1-1)(1+10) = 0×11 = 0 ✓

Common Mistakes

Avoid these frequent errors

Sign errors when solving factor equations
Don't solve (x+10) = 0 as x = 10 instead of x = -10! This gives the wrong x-intercept point. The plus sign means you subtract 10 from both sides. Always move the constant term to isolate x correctly.

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 y = 0 to find x-intercepts?

X-intercepts are points where the graph crosses the x-axis. At these points, the y-coordinate is always 0! So we set the function equal to zero to find where it touches the x-axis.

What if the quadratic isn't already factored?

You'll need to factor it first or use the quadratic formula. Factored form like $y = (x-1)(x+10)$ makes finding x-intercepts much easier using the Zero Product Property.

How do I remember which sign to use when solving?

Think of it as undoing the operation! For $(x-1) = 0$ , add 1 to both sides. For $(x+10) = 0$ , subtract 10 from both sides.

Why are the y-coordinates always 0 for x-intercepts?

By definition, x-intercepts are where the graph crosses the x-axis. Since the x-axis has equation y = 0, all points on it have y-coordinate equal to 0.

Can a quadratic have more than 2 x-intercepts?

No! A quadratic function can have at most 2 x-intercepts. It might have 2 (like this problem), 1 (touches x-axis), or 0 (doesn't cross x-axis).

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Finding Intersection Points: Solve for x in y = (x-1)(x+10)

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 we set y = 0 to find x-intercepts?

What if the quadratic isn't already factored?

How do I remember which sign to use when solving?

Why are the y-coordinates always 0 for x-intercepts?

Can a quadratic have more than 2 x-intercepts?

🌟 Unlock Your Math Potential

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