916.sagews

EXAMPLE 1  Solving a Polynomial Inequality

Solve and graph the solution set on a real number line:  $2x^2 + x > 15$.

f(x) = 2*x^2 + x - 15
solve(f(x) == 0, x)

plot(f, -4, 3)

http://www.wolframalpha.com/input/?i=2x^2+%2B+x+%3E+15

EXAMPLE 2  Solving a Polynomial Inequality

Solve and graph:  $x^3 + x^2 ≤ 4x + 4$.

f(x) = x^3 + x^2 - 4*x - 4
solve(f(x) == 0, x)

plot(f, -3, 3)

http://www.wolframalpha.com/input/?i=x^3+%2B+x^2+%E2%89%A4+4x+%2B+4

EXAMPLE 3  Solving a Rational Inequality

Solve and graph:  $\frac{x + 1}{x + 3} ≥ 2$.

f(x) = (x+1)/(x+3) - 2
f

plot(f, -6, -2, ymin = -10, ymax = 10)

f(x) = (-x - 5)/(x + 3)
f

plot(f, -6, 2, ymin = -10, ymax = 10)

http://www.wolframalpha.com/input/?i=%28x%2B1%29%2F%28x%2B3%29%3E%3D2

EXAMPLE 4  Using the Position Function $s(t) = -16t^2 + v_0t + s_0$

If the initial height $s_0 = 190$ and the initial velocity $v_0 = 96$ feet per second, during what times will the height $s(t) > 190$?

s(t) = -16*t^2 + 96*t + 190

solve(s(t) == 190, t)

h(t) = 190
plot(s, 0, 8) + plot(h, 0, 8)