Convert Quadratic Graph to Algebraic Form: Finding Equation for r=128.048
Question
Find the corresponding algebraic representation for the function
Video Solution
Solution Steps
00:00Choose the appropriate algebraic representation for the function
00:03In the smiling function, the coefficient of X squared is positive
00:07In the sad function, the coefficient of X squared is negative
00:11Let's check the coefficient of each representation
00:14In this case the coefficient is positive, therefore it doesn't suit the function
00:19In this case the coefficient is negative, suitable for the function
00:24In this case the coefficient is positive, therefore it doesn't suit the function
00:28In this case the coefficient is positive, therefore it doesn't suit the function
00:35Let's check the intersection point with the Y-axis
00:41Let's substitute X=0 in the possible representation and check if the intersection point matches
00:49The intersection points are equal, therefore the representation suits the function
00:52And this is the solution to the question
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), implying that at x=0, the maximum value of y is 1. This indicates that the constant term c 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 x2 must be negative. This leads us to the formula y=−x2+c.
Step 3: Construct the Equation – With the downward orientation and the vertex point established, the equation becomes y=−x2+1 as c=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. Thus
Therefore, the algebraic representation of the function is y=−x2+1.