Over which interval is the graph of f(x)= -x^2 +3x+ 8 increasingly

x<1.5

Step-by-step explanation:

The equation is

Use a graphing tool to find the vertex of the parabola.When you get the vertex from the graph, you can now write the increase as ; all x-values less than the x-value of the vertex value in the graph

From the graph, the vertex is at (1.5,10.25), the parabola opens down with maximum value y=10.25

The interval of increase is x<1.5

Step-by-step explanation:

First, the first derivative of the function is computed to distinguish which interval is increasing.

An interval is increasing only if slope is increasing as long as x increases. Then, it is quite evident that curve is increasing for:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

so, converting firstly the mixed fractions to improper fractions and then "adding".