Solve y+10=3x²: Finding Y-Axis Intersection Points

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

The y-axis is where x = 0 on a coordinate plane. So to find where a function crosses the y-axis, we substitute x = 0 into the equation and solve for y.

Q: What's the difference between y-intercept and x-intercept?

Y-intercept: Where the graph crosses the y-axis (set x = 0). X-intercept: Where the graph crosses the x-axis (set y = 0). They're completely different points!

Q: Can a function have more than one y-intercept?

No! A function can only have one y-intercept because for any given x-value (including x = 0), there's only one corresponding y-value in a function.

Q: Why is the answer (0, -10) and not just -10?

Points are written as ordered pairs (x, y). Since we're finding where the function crosses the y-axis, x = 0 and y = -10, giving us the point (0, -10).

Y-Intercepts with Quadratic Functions

At which points does the fuction $y+10=3x^2$ intersect the y axis?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find where the function crosses the Y-axis.

00:12 Remember, at the X-axis, the Y value is zero.

00:16 Now, let's put X equals zero into our equation and solve for Y.

00:27 First, we need to isolate the Y variable.

00:32 This gives us the Y value at the intersection with the Y-axis.

00:36 We started with X equal to zero, remember?

00:42 And that's how we solve this problem!

Step-by-step written solution

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Understand the problem

At which points does the fuction $y+10=3x^2$ intersect the y axis?

Step-by-step solution

To determine the point where the function $y + 10 = 3x^2$ intersects the y-axis, follow these steps:

Step 1: Identify that the y-axis intersection occurs where $x = 0$ .
Step 2: Substitute $x = 0$ into the function equation.
Step 3: Solve for $y$ .

Now, let's go through these steps:

Step 1: Set $x = 0$ .

Step 2: Substitute into the equation:
$y + 10 = 3(0)^2$ , which simplifies to:
$y + 10 = 0$ .

Step 3: Solve for $y$ :
$y = -10$ .

Therefore, the point of intersection with the y-axis is $(0, -10)$ .

Final Answer

$(0,-10)$

Key Points to Remember

Essential concepts to master this topic

Y-Intercept Rule: Set x = 0 to find where function crosses y-axis
Substitution Method: Replace x with 0: y + 10 = 3(0)² becomes y + 10 = 0
Verification: Point (0, -10) means when x = 0, y = -10 ✓

Common Mistakes

Avoid these frequent errors

Setting y = 0 instead of x = 0
Don't set y = 0 to find y-intercept = you get x-intercepts instead! This gives you where the function crosses the x-axis, not the y-axis. Always set x = 0 when finding y-intercepts.

Practice Quiz

Test your knowledge with interactive questions

Find the ascending area of the function

$$ f(x)=2x^2 $$

FAQ

Everything you need to know about this question

Why do we set x = 0 to find the y-intercept?

The y-axis is where x = 0 on a coordinate plane. So to find where a function crosses the y-axis, we substitute x = 0 into the equation and solve for y.

What's the difference between y-intercept and x-intercept?

Y-intercept: Where the graph crosses the y-axis (set x = 0). X-intercept: Where the graph crosses the x-axis (set y = 0). They're completely different points!

Can a function have more than one y-intercept?

No! A function can only have one y-intercept because for any given x-value (including x = 0), there's only one corresponding y-value in a function.

Why is the answer (0, -10) and not just -10?

Points are written as ordered pairs (x, y). Since we're finding where the function crosses the y-axis, x = 0 and y = -10, giving us the point (0, -10).

How do I check if my y-intercept is correct?

Substitute your point back into the original equation. For (0, -10): $(-10) + 10 = 3(0)^2$ gives us $0 = 0$ ✓

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