How many times does the graph of the function below intersect or touch the x-axis? y= -x^2+x+6

Graph of the function touches x-axis twice at 3 and -2.

Step-by-step explanation:

Given : Quadratic function

To find : How many times does the graph of the function given intersect or touch the x-axis?

Solution :

To find the points graph touch the x-axis i.e, the functions real roots.

Using quadratic formula,

General form -

Solution is  

Equation is

where, a=-1 , b=1, c=6

D>0 i.e, 2 real roots exist.

Solution is

Therefore, graph of the function touches x-axis twice at 3 and -2.

Refer the attached figure below.

3x^3-x^2+6x-9

b

step-by-step explanation: