Quadratic Functions

Question

f(x)= -x² +10x-19

a. the domain
b. the vertex
c. the axis of symmetry
d. the x-intercept(s)
e. the y-intercept
f. the maximum or minimum value of the function
h. State the range.
i. State the interval over which the function is decreasing.
j. State the interval over which the function is increasing.

Answer 1

Find the vertex by using x_vertex = -b/(2a) to get its x coordinate; y coordinate is f(x_vertex).

The domain will be all Reals, of course; the range will be(-infinity, y_vertex)

 

The maximum is at the vertex.

 

The function will be increasing from-infinity up to x_vertex and decreasing always thereafter.

 

The y intercept is -19.  You find x intercepts by solving f(x) = 0; if the vertex lies below the x-axis, of course, there are no x-intercepts (in which case Discriminant must have been negative.

 

The axis of symmetry: x = x_vertex.

 

I have given you only a single answer, numerically; I HAVE GIVEN YOU THE METHODS needed to answer each part of your question. I suggest that you study, and even memorize, these principles.