Let's identify the values of a, b, and c in the given quadratic function.
f(x)=4x^2+16x-3
⇕
f(x)= 4x^2+ 16x+( - 3)
We can see above that a= 4, b= 16, and c= - 3. We will now use these values to find the desired information.
Minimum Value
Since a= 4 is greater than 0, the parabola will open upwards. This means it will have a minimum value, which is given by f ( - b2a ). Before we find the value of the function at this point, we need to substitute a= 4 and b= 16 in - b2a.
This tells us that the minimum value of the function is - 19.
Domain and Range
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= 4 is greater than 0, the range is all values greater than or equal to the minimum value, - 19.
Domain:& All real numbers
Range:& y ≥ - 19
Decreasing and Increasing Intervals
Since a= 4 is greater than 0, the function decreases to the left of the minimum value and increases to the right of the minimum value, which we know occurs at x=- 2.
Decreasing Interval:& To the left of - 2
Increasing Interval:& To the right of - 2
Let's identify the values of a, b, and c in the given quadratic function.
h(x)=- x^2+5x+9
⇕
h(x)= - 1x^2+ 5x+ 9
We can see above that a= - 1, b= 5, and c= 9. We will now use these values to find the desired information.
Maximum Value
Since a= - 1 is less than 0, the parabola will open downwards. This means it will have a maximum value, which is given by h ( - b2a ). Before we find the value of the function at this point, we need to substitute a= - 1 and b= 5 in - b2a.
This tells us that the maximum value of the function is 614.
Domain and Range
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 less than 0, the range is all values less than or equal to the maximum value, 614.
Domain:& All real numbers
Range:& y ≤ 61/4
Decreasing and Increasing Intervals
Since a= - 1 is less than 0, the function increases to the left of the maximum value and decreases to the right of the maximum value, which we know occurs at 52.
Increasing Interval:& To the left of 52
Decreasing Interval:& To the right of 52
