Find the Quadratic Equation: Converting Graph at Point (8,-2) to Algebraic Form

Find the corresponding algebraic representation of the drawing:

(8,-2)(8,-2)(8,-2)

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Step-by-step video solution

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00:00 Find the appropriate algebraic representation for the function
00:04 The function is a parabola
00:16 The function is sad (facing down), therefore coefficient A is negative
00:48 The maximum point is 8 units to the right according to the graph, that's how we find P
01:25 The maximum point is 2 units down according to the graph, that's how we find K
01:39 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:

(8,-2)(8,-2)(8,-2)

2

Step-by-step solution

To solve for the algebraic representation of the parabola from the drawing:

  • Step 1: Identify the vertex of the parabola. The drawing indicates the vertex at (8,−2) (8, -2) .
  • Step 2: Write the vertex form of the parabola, y=a(x−h)2+k y = a(x - h)^2 + k , using the vertex (8,−2) (8, -2) as h=8 h = 8 and k=−2 k = -2 .
  • Step 3: Determine the orientation of the parabola. The drawing suggests the parabola opens downward, indicating a negative value for a a . Hence, a<0 a < 0 .
  • Step 4: Substitute the vertex and the orientation into the equation: y=−1(x−8)2−2 y = -1(x - 8)^2 - 2 , simplifying to y=−(x−8)2−2 y = -(x - 8)^2 - 2 .

Therefore, the algebraic representation of the parabola is y=−(x−8)2−2 y = -(x - 8)^2 - 2 .

3

Final Answer

y=−(x−8)2−2 y=-(x-8)^2-2

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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