Convert Quadratic Graph to Algebraic Function: Point (-6) Analysis

Video Solution

Solution Steps

00:00 Choose the appropriate algebraic representation for the function

00:03 Find the intersection point of the function with the Y-axis

00:10 This is the point

00:14 We'll substitute X=0 in each function and compare the intersection points

00:25 According to this representation, the intersection point is different, so not this representation

00:28 Continue with this method for each representation and check the intersection points

00:39 According to this representation, the intersection point is equal, so this representation is correct

00:50 According to this representation, the intersection point is different, so not this representation

01:00 According to this representation, the intersection point is different, so not this representation

01:07 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will determine the vertical shift given to the parent function $y = x^2$ to form the observed parabola.

Identify that the problem involves a vertical translation of the parabola $y = x^2$ .
The function takes the form $y = x^2 + c$ , where $c$ indicates the vertical shift.
From the graph given, it is seen that the vertex of the parabola is situated at $y = -6$ when viewed from the intersection with the y-axis.
This downward shift corresponds to the constant $c$ being negative, specifically $c = -6$ .
By this observation, the function becomes $y = x^2 - 6$ .

Therefore, the solution to the problem is $y = x^2 - 6$ , matching choice 2.