Quadratic Equation: Finding Algebraic Form for Arc Through (-10,-3)

Find the corresponding algebraic representation of the drawing:

(-10,-3)(-10,-3)(-10,-3)

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Step-by-step video solution

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00:00 Find the appropriate algebraic representation for the function
00:03 The function is a parabola
00:23 The minimum point is 10 units left according to the drawing, that's how we find P
01:17 The minimum point is 3 units down according to the drawing, that's how we find K
01:36 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:

(-10,-3)(-10,-3)(-10,-3)

2

Step-by-step solution

To determine the algebraic representation of the parabola, follow these steps:

  • Step 1: Recognize the parabola vertex form, y=(x−p)2+k y = (x - p)^2 + k , which uses (p,k)(p, k) as the vertex.
  • Step 2: Given that the vertex (from the drawing) is (−10,−3)(-10, -3), substitute these values into pp and kk.
  • Step 3: Utilizing vertex form, substitute p=−10p = -10 and k=−3k = -3 into the expression, resulting in: y=(x+10)2−3 y = (x + 10)^2 - 3 .

As a result, the parabola is represented algebraically by replacing (x−p)2(x-p)^2 with (x−(−10))2(x - (-10))^2, simplifying to (x+10)2 (x + 10)^2 , and adding kk, i.e., −3-3.

Therefore, the equation that corresponds with the drawing is y=(x+10)2−3 y = (x + 10)^2 - 3 .

3

Final Answer

y=(x+10)2−3 y=(x+10)^2-3

Practice Quiz

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Which equation represents the function:

\( y=x^2 \)

moved 2 spaces to the right

and 5 spaces upwards.

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