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the factored form for a quadratic function is f(x)=(x‒p)(x‒q). the standard form for a quadratic function is
f(x)=ax^2+bx+c. the factored form for a quadratic function tells us the x-intercepts of the quadratic function, while the standard form for a quadratic function tells us the y-intercept of the quadratic function.

if p=‒1 and q=‒2, use what you have learned about multiplying polynomials to

1) write the factored form of the quadratic

2) write the standard form for the quadratic.

the final equation:

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