Convert Quadratic Graph to Algebraic Form: Finding Equation for r=128.048

Find the corresponding algebraic representation for the function

111

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate algebraic representation for the function
00:03 In the smiling function, the coefficient of X squared is positive
00:07 In the sad function, the coefficient of X squared is negative
00:11 Let's check the coefficient of each representation
00:14 In this case the coefficient is positive, therefore it doesn't suit the function
00:19 In this case the coefficient is negative, suitable for the function
00:24 In this case the coefficient is positive, therefore it doesn't suit the function
00:28 In this case the coefficient is positive, therefore it doesn't suit the function
00:35 Let's check the intersection point with the Y-axis
00:41 Let's substitute X=0 in the possible representation and check if the intersection point matches
00:49 The intersection points are equal, therefore the representation suits the function
00:52 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 corresponding algebraic representation for the function

111

2

Step-by-step solution

This problem involves determining the algebraic representation of a parabola that was presented graphically. Our goal is to interpret the graph and express it in terms of its equation for a downward-opening parabola.

To solve the problem, follow these steps:

  • Step 1: Identify the Parabola's Vertex – According to the diagram, the vertex is positioned at (0,1)(0, 1), implying that at x=0x = 0, the maximum value of yy is 1. This indicates that the constant term cc in the parabola's equation will be 1.
  • Step 2: Determine the Parabola’s Orientation – The given parabola is described as downward-opening. This means the coefficient in front of x2x^2 must be negative. This leads us to the formula y=−x2+cy = -x^2 + c.
  • Step 3: Construct the Equation – With the downward orientation and the vertex point established, the equation becomes y=−x2+1y = -x^2 + 1 as c=1c = 1 from the vertex.

By matching one of the multiple-choice answers with our derived equation, it's clear that choice 2 corresponds to y=−x2+1 y = -x^2 + 1 . Thus

Therefore, the algebraic representation of the function is y=−x2+1 y = -x^2 + 1 .

3

Final Answer

y=−x2+1 y=-x^2+1

Practice Quiz

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One function

\( y=-6x^2 \)

to the corresponding graph:

1234

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