Consider the quadratic equation y = –3x2 – 2x + 4. a. find the value of the discriminant. b. how many real roots does the equation have? c. does the vertex of the graph of the equation lie above, on, or below the x-axis?

In a coastal town, the humidity, measured in grams of water per kilogram of air, increases by 43% for every 1 degree celsius increase in temperature. a scientist observes that the humidity on monday morning is 5.75 grams per kilogram. he wants to know how much the temperature must increase for the humidity to reach at least 49.17 grams per kilogram. let t represent the increase in temperature, in degrees celsius, from monday morning's observation. write an inequality to represent the situation, and use it to determine the desired temperature increase.