As you have seen, sometimes a parabola and a line never intersect. However, if a parabola and a line do intersect, how many different intersection points can they have? How many intersections can two parabolas have? Do two parabolas always intersect? On graph paper, sketch a graph that fits each description below. Not every graph is possible. As you graph, consider the questions above. a. A line and a parabola that intersect twice.
b. A line and a parabola that intersect once.
c. A line and a parabola that intersect more than twice. d. Two parabolas that intersect twice.
e. Two parabolas that have an infinite number of intersections.
f. Two parabolas that never intersect.
g. Two parabolas that only intersect once.

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step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

answer: sorry i can't you.

step-by-step explanation: