Determine the points of intersection of the function
With the X
We have hundreds of course questions with personalized recommendations + Account 100% premium
Determine the points of intersection of the function
With the X
In order to find the point of the intersection with the X-axis, we first need to establish that Y=0.
0 = (x-5)(x+5)
When we have an equation of this type, we know that one of these parentheses must be equal to 0, so we begin by checking the possible options.
x-5 = 0
x = 5
x+5 = 0
x = -5
That is, we have two points of intersection with the x-axis, when we discover their x points, and the y point is already known to us (0, as we placed it):
(5,0)(-5,0)
This is the solution!
The following function has been graphed below:
\( f(x)=-x^2+5x+6 \)
Calculate points A and B.
X-intercepts are points where the graph crosses the x-axis. On the x-axis, the y-coordinate is always 0, so we set y = 0 to find these crossing points.
If two factors multiply to give 0, then at least one factor must equal 0. So if , then either x-5 = 0 OR x+5 = 0 (or both).
By definition, x-intercepts are points where the graph touches or crosses the x-axis. Since every point on the x-axis has a y-coordinate of 0, all x-intercepts have the form (a, 0).
You could expand and solve , but the factored form makes it easier to see the solutions directly!
A quadratic function has at most 2 x-intercepts. Since we found 2 solutions (x = 5 and x = -5), we have found all possible x-intercepts for this function.
Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime