Big Ideas Math Algebra 2, 2014
BI
Big Ideas Math Algebra 2, 2014 View details
7. Transformations of Polynomial Functions
Continue to next subchapter

Exercise 39 Page 210

For the quadratic function the coordinate of the vertex is the maximum value of the function when

Let's identify the values of and in the given quadratic function.
We can see above that and We will now use these values to find the desired information.

Maximum Value

Since is less than the parabola will open downwards. This means it will have a maximum value, which is given by Before we find the value of the function at this point, we need to substitute and in
Substitute values and evaluate
Now we have to calculate To do so, we will substitute for in the given function.
Simplify right-hand side
This tells us that the maximum value of the function is

Domain and Range

Unless there are any specified restrictions on the values, the domain of a quadratic function is all real numbers. Therefore, the domain of this function is all real numbers. Furthermore, since is less than the range is all values less than or equal to the maximum value,

Decreasing and Increasing Intervals

Since is less than the function increases to the left of the maximum value and decreases to the right of the maximum value, which we know occurs at