Nonlinear Functions 3 — Advanced Math

Questions in this quiz (6)

1. The function $$g(x)=(x-1)(x+4)(x-6)^2$$.The value of $$g(2-k)$$ is $$0$$, where $$k$$ is a constant.What is the sum of all possible values of $$k$$?

   • $$3$$
   • $$4$$
   • $$6$$
   • $$2$$

2. A parabola is defined by the function $$f(x)=(x-2)(x+8)$$. What is the $$x$$-coordinate of the vertex?

   • $$-8$$
   • $$-3$$
   • $$2$$
   • $$8$$

3. The area of a trapezoid is equal to $$x^2$$ square centimeters. The two parallel bases of the trapezoid have lengths of $$x+4$$ centimeters and $$x+10$$ centimeters. The height of the trapezoid is $$x-2$$ centimeters. What is the value of $$x$$?

   • $$4$$
   • $$\frac{10}{2}$$
   • $$\frac{14}{5}$$
   • $$5$$

4. The table shows three values of $$x$$ and their corresponding values of $$g(x)$$, where $$g(x)=\frac{q(x)}{x-3}$$ and $$q$$ is a linear function. What is the $$y$$-intercept of the graph of $$y=q(x)$$ in the $$xy$$-plane?

   • $$(0,-12)$$
   • $$(12,0)$$
   • $$(0,6)$$
   • $$(-6,0)$$

5. A billboard has a rectangular display with an area of $$432$$ square feet. If the length of the display is $$3$$ times its height, what is the length of the display, in feet?

   • $$12$$
   • $$24$$
   • $$36$$
   • $$48$$

6. The graph of $$y=3x^2+px+q$$ is shown, where $$p$$ and $$q$$ are constants. The graph has its vertex at $$(-2,-5)$$ and a $$y$$-intercept of $$7$$. What is the value of $$pq$$?

   • $$12$$
   • $$24$$
   • $$48$$
   • $$84$$