Hard Questions

These were taken from the last question (or close to last) of quizzes. Basically any solution that gets the right answer will be here.

Period 4 Quiz 1

Given A(5, 10) and B(10, 4), if point C is on AB and AC is one-third of AB. Determine the equation of another line in slope-intercept form if this line intersects segment AB at C and contains a y-intercept 5.

Period 1 Quiz 1

Using what you had learned in the class to determine the point on the function $$f(x) = -3x^2 + 12x + 9$$ that contains the tangent line which paralells to $$24x - y - 3 = 0$$. (A diagram is recommended but not required!)

Period 4 Quiz 2

Solve $$x$$: $$(x^2 - 3x + 1)^2 - 3(x^2 -3x + 1) = x - 1$$

Period 1 Quiz 2

If $$ax^3 + bx + c$$, with $$a\neq 0, c\neq 0$$, has a factor if the form $$x^2 + px + 1$$, determine the outcome when $$a^2 - c^2$$ in terms of $$a, b, c$$. Shoe some steps.