Determine Intersection Points: Solve y = (x+3)(4x-4) with X-axis

Q: Why do I set y = 0 to find x-axis intersections?

The x-axis is where y = 0! Any point touching the x-axis has coordinates $ (x, 0) $. Setting y = 0 finds all the x-values where the graph crosses this axis.

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

You'll need to factor the quadratic first. Look for two numbers that multiply to give the constant term and add to give the middle coefficient, then use techniques like factoring by grouping.

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

No! A quadratic function can have at most 2 x-intercepts, exactly 1, or none at all. This is because quadratic equations have degree 2, so maximum 2 solutions.

Q: What does it mean when I get the same x-value twice?

This means the parabola touches the x-axis at exactly one point (called a vertex) rather than crossing it. You have a repeated root or double root.

Q: How can I check my answer without substituting?

Look at the factored form: $ y = (x + 3)(4x - 4) $. The x-intercepts are the values that make each factor zero: $ x = -3 $ and $ x = 1 $.

Quadratic Functions with X-axis Intersections

Determine the points of intersection of the function

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

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 point with the X-axis

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

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

00:13 Find what makes each factor equal zero

00:19 This is the first solution

00:31 This is the second solution

00:44 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

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

With the X

Step-by-step solution

To find the points of intersection of the function $y = (x+3)(4x-4)$ with the x-axis, we set $y = 0$ and solve for $x$ .

First, we set each factor of the expression to zero:

For the first factor, $x+3 = 0$ :

Solve for $x$ :

$x + 3 = 0$
$x = -3$

For the second factor, $4x-4 = 0$ :

Solve for $x$ :

$4x - 4 = 0$
$4x = 4$
$x = 1$

The points of intersection are where these $x$ values occur with $y = 0$ . Thus, the points are $(-3, 0)$ and $(1, 0)$ .

Therefore, the solution to the problem is $(-3,0),(1,0)$ .

Final Answer

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

Key Points to Remember

Essential concepts to master this topic

Zero Product Property: If $ab = 0$ , then $a = 0$ or $b = 0$
Factored Form: Set each factor to zero: $x + 3 = 0$ gives $x = -3$
Verify: Check that both points have y-coordinate of 0: $(-3, 0)$ and $(1, 0)$ ✓

Common Mistakes

Avoid these frequent errors

Confusing x-intercepts with y-intercepts
Don't look for points where x = 0 when finding x-axis intersections = gives (0, y) points instead! This confuses axes and gives coordinates like (0, 3). Always set y = 0 to find x-intercepts, which have coordinates (x, 0).

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 y = 0 to find x-axis intersections?

The x-axis is where y = 0! Any point touching the x-axis has coordinates $(x, 0)$ . Setting y = 0 finds all the x-values where the graph crosses this axis.

What if the function isn't already factored?

You'll need to factor the quadratic first. Look for two numbers that multiply to give the constant term and add to give the middle coefficient, then use techniques like factoring by grouping.

Can a quadratic have more than 2 x-intercepts?

No! A quadratic function can have at most 2 x-intercepts, exactly 1, or none at all. This is because quadratic equations have degree 2, so maximum 2 solutions.

What does it mean when I get the same x-value twice?

This means the parabola touches the x-axis at exactly one point (called a vertex) rather than crossing it. You have a repeated root or double root.

How can I check my answer without substituting?

Look at the factored form: $y = (x + 3)(4x - 4)$ . The x-intercepts are the values that make each factor zero: $x = -3$ and $x = 1$ .

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Determine Intersection Points: Solve y = (x+3)(4x-4) with X-axis

Quadratic Functions with X-axis Intersections

❤️ 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 y = 0 to find x-axis intersections?

What if the function isn't already factored?

Can a quadratic have more than 2 x-intercepts?

What does it mean when I get the same x-value twice?

How can I check my answer without substituting?

🌟 Unlock Your Math Potential

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