Solve (x+4)² - 1: Finding Y-Axis Intersection Points

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

The y-axis is where x = 0! Every point on the y-axis has an x-coordinate of 0. So to find where our function crosses the y-axis, we substitute x = 0 into the equation.

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

Y-intercept: Set x = 0, solve for y (point is (0, y))X-intercept: Set y = 0, solve for x (point is (x, 0))

Q: How do I write the final answer as a point?

Y-intercepts are always written as (0, y-value). Since we found y = 15 when x = 0, the point is (0, 15).

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

No! Every function can only cross the y-axis at most once. This is because for any x-value (including x = 0), a function gives exactly one y-value.

Y-Intercepts with Quadratic Substitution

Find the intersection of the function

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

With the Y

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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 Y-axis

00:03 Substitute X=0 and solve to find the intersection point

00:13 Let's calculate

00:23 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

Find the intersection of the function

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

With the Y

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the equation of the function $y = (x+4)^2 - 1$ .
Step 2: Since we're finding the intersection with the Y-axis, set $x = 0$ .
Step 3: Substitute $x = 0$ into the equation and solve for $y$ .

Now, let's work through each step:

Step 1: The equation of the function is already given as $y = (x+4)^2 - 1$ .

Step 2: To find the Y-intercept, let $x = 0$ .

Step 3: Substitute $x = 0$ into the equation:

$\begin{aligned} y &= (0 + 4)^2 - 1 \\ &= 4^2 - 1 \\ &= 16 - 1 \\ &= 15 \end{aligned}$

Therefore, the intersection with the Y-axis is at $(0, 15)$ .

Final Answer

$(0,15)$

Key Points to Remember

Essential concepts to master this topic

Y-Intercept Rule: Set x = 0 to find where function crosses y-axis
Substitution: Replace x with 0: (0+4)² - 1 = 16 - 1 = 15
Verification: Point (0,15) means when x=0, y=15 which matches our calculation ✓

Common Mistakes

Avoid these frequent errors

Setting y = 0 instead of x = 0
Don't set y = 0 when finding y-intercepts = you'll get x-intercepts instead! This gives completely different points on the wrong axis. Always set x = 0 for y-intercepts and y = 0 for x-intercepts.

Practice Quiz

Test your knowledge with interactive questions

Find the corresponding algebraic representation of the drawing:

FAQ

Everything you need to know about this question

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

The y-axis is where x = 0! Every point on the y-axis has an x-coordinate of 0. So to find where our function crosses the y-axis, we substitute x = 0 into the equation.

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

Y-intercept: Set x = 0, solve for y (point is (0, y))
X-intercept: Set y = 0, solve for x (point is (x, 0))

How do I write the final answer as a point?

Y-intercepts are always written as (0, y-value). Since we found y = 15 when x = 0, the point is (0, 15).

What if I get a negative y-value?

That's completely normal! A negative y-value just means the function crosses the y-axis below the x-axis. The point would be (0, negative number).

Can a function have more than one y-intercept?

No! Every function can only cross the y-axis at most once. This is because for any x-value (including x = 0), a function gives exactly one y-value.

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