Which ordered pair is a solution of the equation?
Y = -3x - 4

A) f(x) = -16*(x + 0.125)*(x - 1.5)

B) points (-0.125, 0) and (1.5, 0)

C) tends to negative infinity

D) Draw the line that pass through the roots from item B and has (0.6875, 10.5625) as a vertex.

Step-by-step explanation:

A) To factor a parabola we need to find its roots. We can do that with the quadratic formula:

The factored form is:

f(x) = a*(x -x1)*(x - x2)

then:

f(x) = -16*(x + 0.125)*(x - 1.5)

B) the x-intercepts are its roots, for this case the points (-0.125, 0) and (1.5, 0)

C) Given that the coefficient a of the parabola is negative (-16) then the function open downward. As a consequence its end behaviour tends to negative infinity.

D) To graph f(x) we need 3 points, given that we already have 2 roots, then we need 1 point. One option is calculate the vertex, as follows:

x-component of the vertex of a parabola: -b/(2a)

x-component of the vertex of a parabola: -22/[2(-16)] = 0.6875

The y-component of the vertex of a parabola is obtained replacing the x-component in the formula:

y-component = −16(0.6875)^2 + 22(0.6875) + 3 = 10.5625

So, the vertex coordinate is (0.6875, 10.5625)