Quadratic Function: Finding Algebraic Equation for Graph at Point (0,-4)

Quadratic Functions with Vertex Form Identification

Find the corresponding algebraic representation of the drawing:

(0,-4)(0,-4)(0,-4)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find appropriate algebraic representation for the function
00:04 The function is a parabola
00:15 The minimum point is 4 down according to the graph, that's how we'll find K
00:45 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Find the corresponding algebraic representation of the drawing:

(0,-4)(0,-4)(0,-4)

2

Step-by-step solution

To solve this problem, let us first note that the labeled point is (0,4)(0, -4), which suggests the parabola touches or intersects the y-axis at this point. Without more information indicating horizontal translation, it is reasonable to assume this is the vertex of the parabola, pointing down a simple transformation from y=x2y=x^2 to y=x24y=x^2-4.

Given the simplicity and symmetry (likely no xx coefficient subtracted or added), this directly translates to a parabola form with only a vertical shift downward.

Therefore, the algebraic representation of the given parabolic drawing is y=x24 y = x^2 - 4 .

The correct choice corresponding to this is y=x24 y = x^2 - 4 .

3

Final Answer

y=x24 y=x^2-4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Use given point to determine vertical shift in parabola
  • Technique: Point (0,-4) means y-intercept shifts from y=x2 y=x^2 to y=x24 y=x^2-4
  • Check: Substitute x=0: y=024=4 y=0^2-4=-4 matches given point ✓

Common Mistakes

Avoid these frequent errors
  • Confusing vertical shift direction with sign
    Don't think point (0,-4) means y=x2+4 y=x^2+4 = wrong direction! The negative y-value means the parabola shifts DOWN, not up. Always remember: negative y-intercept means subtract from the basic form.

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

How do I know if it's a vertical shift and not horizontal?

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When the given point has x = 0, it's on the y-axis! This tells us about vertical shifts. The y-coordinate directly shows how far up or down the basic parabola y=x2 y=x^2 has moved.

Why isn't the answer y=x2+4 y=x^2+4 ?

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Because the point is at (0, -4), not (0, 4)! The negative sign means the parabola is 4 units below the basic y=x2 y=x^2 curve, so we subtract 4.

Could there be other transformations I'm missing?

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From just one point, we assume the simplest transformation. Since (0, -4) is likely the vertex and the parabola appears symmetric, we only need a vertical shift: y=x24 y=x^2-4 .

How can I verify this is the right equation?

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Substitute the given point! For y=x24 y=x^2-4 , when x=0: y=024=4 y=0^2-4=-4 . This matches the point (0, -4) perfectly!

What if the parabola opened downward instead?

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If it opened downward, the equation would be y=x24 y=-x^2-4 . But looking at the graph, this parabola opens upward, so we keep the positive x2 x^2 term.

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