What is a Vertex?
A vertex is the maximum or minimum point of a parabola. A max/min point is the midpoint and is the highest or lowest point of a graph.
The vertex is a coordinate pair (x,y).
The vertex is a coordinate pair (x,y).
As seen above, the LOS/ AOS goes directly through the vertex of the parabola. The AOS only has a x- value since its y-value will always equal 0. (y=0)
This implies that since the AOS will always pass through the vertex and its y-value will always equals 0, leaving only the x-value...............the AOS= the x-value of the coordinate pair.
The picture above proves this. As you can see, the AOS clearly passes through the 2 on the x-axis meaning that x=2/ the AOS is 2.
When you look at the x-value of the coordinate pair of the vertex, it is also 2.
This implies that since the AOS will always pass through the vertex and its y-value will always equals 0, leaving only the x-value...............the AOS= the x-value of the coordinate pair.
The picture above proves this. As you can see, the AOS clearly passes through the 2 on the x-axis meaning that x=2/ the AOS is 2.
When you look at the x-value of the coordinate pair of the vertex, it is also 2.
Because of this, you are able to use the equation to find the AOS, to instead find the x-value of the parabola.
The equation to find the AOS is..........X= -B/2A
....................This same equation can be used to find the x-value of the vertex's coordinate pair because the AOS= the x-value of the coordinate pair.
Then, after finding the X-value of the coordinate pair, you plug it into the quadratic equation.
y= ax² + bx + c
The equation to find the AOS is..........X= -B/2A
....................This same equation can be used to find the x-value of the vertex's coordinate pair because the AOS= the x-value of the coordinate pair.
Then, after finding the X-value of the coordinate pair, you plug it into the quadratic equation.
y= ax² + bx + c
Example:
y= 2x² - 4x + 5
a= 2 b= -4 c= 5 a= 2 , b= -4 x= -(-4) / 2 (2) 4/ 4 = 1 AOS= 1 y= 2x² - 4x + 5 y= 2(1)² - 4(1)+ 5 1x1=1 -4x 1= -4 y= 2(1) - 4 + 5 y= 2 - 4 + 5 y= 3 Vertex = (1,3) |
1. Label the "A", "B", and "C" value of the quadratic equation.
2. Plug the "A" and "B" values into the AOS equation, and Solve for X. (The 'B" value has become a positive because two negatives make a positive. Since it was originally -4, when you add the (-) in front of it, it becomes a positive 4.) 3. Plug the X-value/ AOS into the quadratic equation, and solve for Y. 4. Write the vertex as a coordinate pair and graph. |
What else can you tell me about this graph and the equation?
y- intercept = (0,5)
x-intercept = no solutions
y- intercept = (0,5)
x-intercept = no solutions