a Use the formula for the line of symmetry to get the x -coordinate of the vertex, then substitute that into the function to get the y-coordinate.
B
b Look for increasing and decreasing y-values to determine where the function is symmetric.
A
a (0,4)
B
b (0,-6)
Practice makes perfect
a For this exercise, we can use the properties of a quadratic to solve for the vertex. Recall that the axis of symmetry passes through the vertex of a quadratic function. Let's start by comparing our function, y=x^2+4, to the standard quadratic function.
ccc
y&=& ax^2&+& bx&+&c
↕ & & ↕ & & ↕ & & ↕
y&=& 1x^2&+& 0x& + & 4
In order to find vertex, of a quadratic in standard form we will need to first find the axis of symmetry.
x=- b/2 a
In our case we can substitute a= 1, b= 0, and c=4.
From this, we can conclude that the y-coordinate for our vertex is 4 and the vertex is (0,4).
b For this part, we will graph the elements of the table on a coordinate plane to see the vertex. We need to analyze the table of values to determine the vertex of the quadratic. We can see where the vertex is if we plot the points from the table.
x
-2
-1
0
1
2
y
-14
-8
-6
-8
-14
Although some people can see the symmetry by looking at the table, it's much clearer when we look at the points on the graph.
In this case, a vertical line through the point (0,-6) creates the axis of symmetry. From that, we can conclude that (0,-6) is our vertex.
