Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. he graphs the expressions. what is the greatest possible number of intersections for these graphs? none one two infinite

Consider any quadratic equation

A x² + Bx +c=0

and other a linear expression like , p x + q =0

When we combine them , as both of them are equal to zero so the equation becomes

→ A x² + Bx +c = p x +q

1. Graph of quadratic expression is parabolic. It cuts the coordinate axis at two different points if both the roots are real and unequal and if you graph a linear expressions it will be a line.

2. So, a line can cut the parabola or quadratic, maximum at two points.

Maximum number of possible intersections=2

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for