Consider the function

Question

Consider the function f(x) = -x² - 6x + 9.

a. Find the vertex of the graph of the function.

b. Find the x-intercepts of the graph. Use exact values that are completely simplified.

c. Find the x-intercepts of the graph. Use decimal approximations rounded to the nearest thousandth.

Answer 1

The x coordinate of the vertex is given by x = -b/(2a).  Once you have that, substitute; y = f(x).

 

To find x-intercepts by using the quadratic formula.  Firt, calculate Discriminant, D = b²-4ac. I get 72.

Its square root is 6√2 so that will participate in your calculation of the two x-intercepts.

They can be converted into decimal values.

 

Remember: x = (-b±√D)/(2a) is the correct way to parenthesize the expressions for x-intercepts (root of f(x) = 0).