a Start by identifying a, b, and c. The maximum value of the given quadratic function is f ( - b2a ).
B
b Start by identifying a, b, and c. The maximum value of the given quadratic function is f ( - b2a ).
C
c Start by identifying a, b, and c. The maximum value of the given quadratic function is f ( - b2a ).
A
aMinimum
B
b -48
C
cDomain: {All real numbers} Range: {y | y ≥ - 48}
Practice makes perfect
a For a quadratic function y=ax^2+bx+c, the y-coordinate of the vertex is the minimum value of the function when a>0.
Let's identify the values of a, b, and c in the given quadratic function.
y=3x^2+18x-21
⇕
f(x)= 3x^2+ 18x+( - 21)
We can see above that a= 3, b= 18, and c= - 21. We will now use these values to find the desired information. Since a= 3 is greater than 0, the parabola will open upwards. This means it will have a minimum value.
b The minimum value is given by substituting - b2a for x. Before we find the value of the function at this point, we need to substitute a= 3 and b= 18 in - b2a.
This tells us that the minimum value of the function is - 48.
c Unless there are any specified restrictions on the x-values, the domain of a quadratic function is all real numbers. Therefore, the domain of this function is all real numbers. Furthermore, since a= 3 is greater than 0, the range is all values greater than or equal to the minimum value, - 48.
Domain:& {All real numbers}
Range:& {y | y ≥ - 48}
