Find Y-Intercept of y=(x+3)²: Quadratic Function Analysis

Y-Intercept Finding with Quadratic Functions

Find the intersection of the function

y=(x+3)2 y=(x+3)^2

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 of the function with the Y-axis
00:03 At the intersection point with the Y-axis, X = 0
00:07 Therefore, we substitute X = 0 and solve to find the intersection point with the Y-axis
00:16 This is the Y value at the intersection point, we substitute X=0 as we did at the point
00:23 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the intersection of the function

y=(x+3)2 y=(x+3)^2

With the Y

2

Step-by-step solution

To find the intersection of the parabola y=(x+3)2 y = (x+3)^2 with the y-axis, we set x=0 x = 0 since any point on the y-axis has its x-coordinate as zero.

Step-by-step solution:

  • Step 1: Substitute x=0 x = 0 into the equation: y=(0+3)2 y = (0+3)^2 .
  • Step 2: Simplify the expression:
  • y=(3)2 y = (3)^2
  • y=9 y = 9

Therefore, the intersection point of the parabola with the y-axis is (0,9)(0, 9).

Accordingly, among the given choices, the correct choice for the intersection is (0,9)(0, 9).

3

Final Answer

(0,9) (0,9)

Key Points to Remember

Essential concepts to master this topic
  • Y-Intercept Rule: Set x = 0 and solve for y
  • Technique: Substitute: y = (0+3)² = 3² = 9
  • Check: Point (0,9) has x-coordinate 0, confirming it's on y-axis ✓

Common Mistakes

Avoid these frequent errors
  • Confusing x-intercept with y-intercept
    Don't set y = 0 to find y-intercept = wrong axis intersection! This finds where the parabola crosses the x-axis instead. Always set x = 0 to find where the function crosses the y-axis.

Practice Quiz

Test your knowledge with interactive questions

Find the intersection of the function

\( y=(x-2)^2 \)

With the X

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 for every point! To find where any function crosses the y-axis, we substitute x = 0 and solve for the y-value.

What's the difference between (0,9) and (9,0)?

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(0,9) means x = 0, y = 9 (y-intercept). (9,0) means x = 9, y = 0 (x-intercept). Remember: (x-coordinate, y-coordinate) order matters!

How do I expand (x+3)² when x = 0?

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Just substitute first: (0+3)2=32=9 (0+3)^2 = 3^2 = 9 . No need to expand the binomial when you're plugging in a specific value!

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

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

What if I get a negative y-intercept?

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That's perfectly normal! The y-intercept can be positive, negative, or zero. It just tells you whether the parabola crosses above, below, or through the origin.

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