Start by identifying a, b, and c. If a>0, the parabola has a minimum value. If a<0, it has a maximum value.
B
b
The minimum or maximum value of the given quadratic function is obtained by substituting the values given in the equation into the formula - b2a.
C
c
Use the maximum or minimum value to determine the range.
A
a
Minimum
B
b
0
C
c
Domain: All real numbers Range: {y|y ≥ 0}
Practice makes perfect
a
Let's identify the values of a, b, and c in the given quadratic function.
y=x^2-4x+4
⇕
y= 1x^2+( -4)x+ 4
We can see above that a= 1, b= -4, and c= 4. Since a>0, the parabola will have a minimum value.
b
Since a= 1 is greater than 0, the parabola will open upwards. This means it will have a minimum value. To find it, we will evaluate the given function at x=- b2 a. Before we find the value of the function at this point, we need to substitute a= 1 and b= -4 in - b2 a.
This tells us that the minimum value of the function is 0.
c
Unless there are any specified restrictions on the x-values, the domain of a quadratic function is all real numbers. Furthermore, since the minimum value of the function is y=0, the range is all values greater than or equal to 0.
