Quadratics — Quiz 1

Questions in this quiz (11)

1. If $$x^2 = -(x - 4)(x + 4)$$ then one possible value of $$x$$ could be:

   • $$\sqrt{2}$$
   • $$-2\sqrt{2}$$
   • $$-2$$
   • $$4$$

2. Given the quadratic equation: $$y=3x^2+5x+7$$which of the following characterizes the roots of this equation?

   • Two real roots
   • Two complex roots
   • No roots
   • One real root

3. If $$y = 3x^2 - 4x$$, what is a value for $$y$$ when $$x$$ and $$y$$ are equal?

   • 3
   • $$5 , \frac{3}{5}$$
   • $$3 , 5$$
   • $$0 , \frac{5}{3}$$

4. What are the solutions to the following equation?$$3x^2 + 5x - 2 = 0$$

   • $$\frac{1}{3}, -2$$
   • $$3, -2$$
   • $$\frac{1}{2}, 2$$
   • $$\frac{1}{3}, -3$$

5. When $$3x^3z^2 - 4x^2 = 72$$ and the value of $$x$$ is 2, what is the value of $$z$$ given that $$z$$ is positive?

   • $$\sqrt{3}$$
   • $$\frac{11}{3}$$
   • $$\frac{72}{24}$$
   • $$\sqrt{\frac{11}{3}}$$

6. What condition must be true about the constants $$a$$, $$b$$, and $$c$$ in the quadratic equation $$ax^2 + bx + c = 0$$so that the equation has exactly one real solution?

   • $$b^2 - 4ac$$ > $$0$$
   • $$b^2 - 4ac$$ < $$0$$
   • $$b^2 - 4ac = 0$$
   • $$b^2 - 4ac \leq 0$$

7. Write the quadratic equation in vertex form (standard form): $$y=x^2-4x+3$$(Recall: Vertex form is $$y=a(x-h)^2+k$$)

   • $$y=2(x-2)^2+1$$
   • $$y=(x-2)^2-1$$
   • $$y=(x-1)^2-2$$
   • $$y=(x-1)^2+2$$

8. A quadratic function $$y=f(x)$$ satisfies $$f(2)=f(8)$$. Find its axis of symmetry.

   • $$x=2$$
   • $$x=-8$$
   • $$x=5$$
   • $$x=-2$$

9. Solve quadratic equations: $$3x^2+5x-2=0$$

   • $${-\frac{1}{3}, -6}$$
   • $${\frac{1}{3}, -2}$$
   • $${\frac{1}{3}, -6}$$
   • $${-2}$$

10. Solve quadratic equations: $$(x+3)(x-4)=7$$

    • $${\frac{1-\sqrt{77}}{2}, 1+\sqrt{77}}$$
    • $${\frac{-1+\sqrt{77}}{2}, \frac{-1-\sqrt{77}}{2}}$$
    • $${\frac{-1+\sqrt{77}}{2}, \frac{1+\sqrt{77}}{2}}$$
    • $${\frac{1+\sqrt{77}}{2}, \frac{1-\sqrt{77}}{2}}$$

11. Solve the equation: $$(2x+5)^2=36$$

    • $${-\frac{1}{2}, \frac{1}{2}}$$
    • $${\frac{1}{2}, -\frac{11}{2}}$$
    • $${-\frac{1}{2}, \frac{11}{2}}$$
    • $${\frac{1}{2}, -\frac{11}{2}}$$