Where do the roots of a quadratic function exist on a graph and what is the value for the output for all roots?

If the graph of the quadratic function y = a x 2 + b x + c crosses the -axis, the values of at the crossing points are the roots or solutions of the equation. If the equation a x 2 + b x + c = 0 has just one solution (a repeated root) then the graph just touches the -axis without crossing it.

Step-by-step explanation:

100% on edg. :)

.25

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is