Find the Algebraic Equation: Quadratic Function with Radius 6

Question

Find the corresponding algebraic representation for the function

666

Video Solution

Solution Steps

00:00 Choose the appropriate algebraic representation for the function
00:03 In a sad function, the coefficient of X squared is negative
00:07 Conversely, in a smiling function, the coefficient of X squared is positive
00:13 In this case, the coefficient is positive so it doesn't fit the function
00:22 In this case, the coefficient is negative, it fits
00:27 In this case, the coefficient is positive so it doesn't fit the function
00:32 And in this case too, the coefficient is positive, it doesn't fit
00:35 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we need to identify the algebraic representation of the given graph of a function. Based on the observation of the parabola, which opens downward and intersects the y-axis at the point y=6 y = 6 , we can deduce its form.

Step 1: Identify the type of parabola.
The graph shows a parabola opening downwards, indicating that the leading coefficient a a in the equation y=ax2+c y = ax^2 + c is negative.

Step 2: Identify key points on the graph.
Since the parabola intersects the y-axis at y=6 y = 6 , this means when x=0 x = 0 , y=6 y = 6 . Thus, the equation y=ax2+c y = ax^2 + c simplifies to y=−x2+6 y = -x^2 + 6 .

Step 3: Confirmation of the algebraic representation.
From the downward orientation and the vertical intersection at y=6 y = 6 without any lateral shifts, the equation y=−x2+6 y = -x^2 + 6 fully describes the parabola.

Therefore, the corresponding algebraic representation of the function is y=−x2+6 y = -x^2 + 6 .

Answer

y=−x2+6 y=-x^2+6

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