Find Y-Intercept of (x-7)²-40: Quadratic Function Analysis

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

The y-axis is where x = 0! So to find where your function crosses the y-axis, you substitute x = 0 and solve for y. This gives you the point (0, y-value).

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

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

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

No! Every function can only cross the y-axis once because there's only one y-value when x = 0. However, quadratics can have 0, 1, or 2 x-intercepts.

Y-Intercept with Vertex Form Functions

Find the intersection of the function

$y=(x-7)^2-40$

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

00:04 Substitute X=0 and solve to find the intersection point

00:11 Let's calculate

00:26 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

$y=(x-7)^2-40$

With the Y

Step-by-step solution

To find the intersection of the function $y = (x - 7)^2 - 40$ with the $y$ -axis, we set $x = 0$ since this is the defining property of the $y$ -axis.

Substitute $x = 0$ into the function:

Compute $y = (0 - 7)^2 - 40$ .
Calculate $y = (-7)^2 - 40$ .
This simplifies to $y = 49 - 40$ .
Thus, $y = 9$ .

The point of intersection on the $y$ -axis is therefore $(0, 9)$ .

Therefore, the solution to the problem is $(0, 9)$ .

Final Answer

$(0,9)$

Key Points to Remember

Essential concepts to master this topic

Y-Intercept Rule: Set x = 0 to find where function crosses y-axis
Technique: Substitute x = 0: y = (0-7)² - 40 = 49 - 40 = 9
Check: Point (0,9) means when x = 0, y = 9 ✓

Common Mistakes

Avoid these frequent errors

Setting y = 0 instead of x = 0
Don't set y = 0 to find y-intercept = this finds x-intercepts instead! This confuses where the graph crosses axes and gives wrong coordinates. Always set x = 0 for y-intercept and y = 0 for x-intercepts.

Practice Quiz

Test your knowledge with interactive questions

Which equation represents the function:

$$ y=x^2 $$

moved 2 spaces to the right

and 5 spaces upwards.

FAQ

Everything you need to know about this question

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

The y-axis is where x = 0! So to find where your function crosses the y-axis, you substitute x = 0 and solve for y. This gives you the point (0, y-value).

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

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

Can a quadratic function have more than one y-intercept?

No! Every function can only cross the y-axis once because there's only one y-value when x = 0. However, quadratics can have 0, 1, or 2 x-intercepts.

How do I know if my y-intercept point is correct?

Substitute your coordinates back into the original equation! If $(0,9)$ is correct, then $9 = (0-7)^2 - 40$ should be true.

What if I get a negative y-intercept?

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

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