Find Intersection Points of y = (4x+1)(x-2) with the X-Axis

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 height (y-value) is always zero! So we solve $ y = 0 $ to find where this happens.

Q: What is the Zero Product Property exactly?

If two numbers multiply to give zero, then at least one of them must be zero. So if $ (4x+1)(x-2) = 0 $, then either $ 4x+1 = 0 $ or $ x-2 = 0 $ (or both).

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

No! Keep it factored - that's the whole point! Expanding $ (4x+1)(x-2) $ would give you a quadratic to factor again. The factored form makes solving much easier.

Q: How do I solve 4x + 1 = 0?

Subtract 1 from both sides: $ 4x = -1 $, then divide by 4: $ x = -\frac{1}{4} $. Remember to include the y-coordinate 0 for the final point!

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

Never! A quadratic function can have at most 2 x-intercepts. It could have exactly 2 (like this problem), exactly 1, or even 0 x-intercepts depending on where the parabola sits.

Quadratic Functions with X-Axis Intersections

Determine the points of intersection of the function

$y=(4x+1)(x-2)$

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 our line crosses the X-axis.

00:13 Remember, at these points, the Y value is zero.

00:17 So, set Y to zero and solve the equation to find X.

00:23 Look for values that make each part of the equation zero.

00:29 Great! We found one solution here.

00:45 And here's another solution.

00:50 That's how we solve this problem. Well done!

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

$y=(4x+1)(x-2)$

With the X

Step-by-step solution

To find the points of intersection of the function $y = (4x+1)(x-2)$ with the x-axis, we need to solve this equation where $y = 0$ . Therefore, we set $(4x+1)(x-2) = 0$ .

By applying the Zero Product Property, we know that either $4x+1 = 0$ or $x-2 = 0$ .

Solving the first equation $4x+1 = 0$ , we have:

4x = -1 \Rightarrow x = -\frac{1}{4}

Solving the second equation $x-2 = 0$ , we have:

x = 2

Therefore, the points of intersection with the x-axis, where the function equals zero, are $(-\frac{1}{4}, 0)$ and $(2, 0)$ .

Thus, the solution to the problem is $(2,0),(-\frac{1}{4},0)$ .

Final Answer

$(2,0),(-\frac{1}{4},0)$

Key Points to Remember

Essential concepts to master this topic

Rule: Set y = 0 to find x-axis intersection points
Technique: Use Zero Product Property: if (4x+1)(x-2) = 0, then 4x+1 = 0 or x-2 = 0
Check: Substitute x-values: (-1/4, 0) and (2, 0) both make y = 0 ✓

Common Mistakes

Avoid these frequent errors

Setting each factor equal to y instead of zero
Don't solve 4x+1 = y and x-2 = y when finding x-intercepts = wrong coordinates! This gives you random points, not where the graph crosses the x-axis. Always set the entire expression equal to zero: (4x+1)(x-2) = 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 we set y = 0 to find x-intercepts?

X-intercepts are points where the graph crosses the x-axis. At these points, the height (y-value) is always zero! So we solve $y = 0$ to find where this happens.

What is the Zero Product Property exactly?

If two numbers multiply to give zero, then at least one of them must be zero. So if $(4x+1)(x-2) = 0$ , then either $4x+1 = 0$ or $x-2 = 0$ (or both).

Do I need to expand the factored form first?

No! Keep it factored - that's the whole point! Expanding $(4x+1)(x-2)$ would give you a quadratic to factor again. The factored form makes solving much easier.

How do I solve 4x + 1 = 0?

Subtract 1 from both sides: $4x = -1$ , then divide by 4: $x = -\frac{1}{4}$ . Remember to include the y-coordinate 0 for the final point!

Can a quadratic function have more than 2 x-intercepts?

Never! A quadratic function can have at most 2 x-intercepts. It could have exactly 2 (like this problem), exactly 1, or even 0 x-intercepts depending on where the parabola sits.

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Find Intersection Points of y = (4x+1)(x-2) with the 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 we set y = 0 to find x-intercepts?

What is the Zero Product Property exactly?

Do I need to expand the factored form first?

How do I solve 4x + 1 = 0?

Can a quadratic function have more than 2 x-intercepts?

🌟 Unlock Your Math Potential

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