Identify the Graph of y=x²-9: Quadratic Function Recognition

Video Solution

Solution Steps

00:00 Match the function to the appropriate graph

00:03 Notice the coefficient of X squared is positive, therefore the function is smiling

00:09 We want to find the intersection point with the Y-axis

00:12 Substitute X=0 and solve to find the intersection point with Y-axis

00:17 This is the intersection point with the Y-axis

00:20 Now let's find the intersection point with the X-axis

00:23 Substitute Y=0 to find the intersection point with the X-axis

00:27 Isolate X

00:30 Take the square root

00:35 When taking square root there are 2 solutions (positive and negative)

00:40 These are the intersection points with the X-axis

00:46 Let's draw the graph according to the function type and intersection points we found

00:57 And this is the solution to the question

Step-by-Step Solution

To solve the problem of identifying which chart represents the function $y = x^2 - 9$ , let's analyze the function and its graph:

The function $y = x^2 - 9$ is a parabola that can be described by the general form $y = x^2 + k$ where $k = -9$ .
It is a standard upward-opening parabola with its vertex located at the point $(0, -9)$ . This is because there is no coefficient affecting $x$ , so horizontally it is centered at the origin.
To find the correct graph, we look for one where the bottommost point of the parabola is at $(0, -9)$ . This point, known as the vertex, should sit on the y-axis and be the lowest point of the curve due to the upward opening.

After inspecting the charts:

Chart 4 depicts a parabola opening upwards, with its vertex at $(0, -9)$ . This aligns perfectly with the form and properties of our function $y = x^2 - 9$ .

Therefore, the chart that represents the function $y = x^2 - 9$ is Choice 4.