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 -9
C
cDomain: {All real numbers} Range: {y | y ≥ - 9}
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=x^2+4x-5
⇕
y= 1x^2+ 4x+( - 5)
We can see above that a= 1, b= 4, and c= - 5. We will now use these values to find the desired information. Since a= 1 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= 1 and b= 4 in - b2a.
This tells us that the minimum value of the function is - 9.
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= 1 is greater than 0, the range is all values greater than or equal to the minimum value, - 9.
Domain:& {All real numbers}
Range:& {y | y ≥ - 9}
