Interactive practice questions
Consider the function $f\left(x\right)=x^2-4x+9$f(x)=x2−4x+9.
The leading coefficient of $f\left(x\right)$f(x) is:
Positive
Negative
Hence state the nature of the turning point of this quadratic function.
Maximum
Minimum
Determine the equation for $f'\left(x\right)$f′(x).
Enter each line of work as an equation.
Determine the equation for $f''\left(x\right)$f′′(x).
Enter each line of work as an equation.
Use your result from part (d) to select the correct statement.
The constant value of $f''\left(x\right)$f′′(x) indicates that $f\left(x\right)$f(x) is always concave down, indicating a maximum turning point.
The constant value of $f''\left(x\right)$f′′(x) indicates that $f\left(x\right)$f(x) is always concave up, indicating a minimum turning point.
Consider the function $f\left(x\right)=-x^2+4x-9$f(x)=−x2+4x−9.
Consider the function $f\left(x\right)=\left(x-5\right)^2+3$f(x)=(x−5)2+3.
Consider the function $f\left(x\right)=-\left(x-5\right)^2-4$f(x)=−(x−5)2−4.