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Quadratic Expressions and Equations Review (Grade 10)

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Quadratic Expressions and Equations Review

1. 
The lowest or highest point on a parabola is the                 .
  1. vertex
  2. slope
  3. axis of symmetry
  4. y-axis
2. 
For [math] y=ax^2+bx+c [/math], if a > 0, then the parabola opens           , but if a < 0, then the parabola opens               .
3. 
Which equation represents the parabola shown below?
Graph - Quadratic Function y=-2x^2
  1. [math]y = 1/2 x^2 [/math]
  2. [math]y = -1/2 x^2 [/math]
  3. [math]y=2x^2[/math]
  4. [math]y=-2x^2[/math]
4. 
How many real solutions does the equation [math]4x^2 + 4x +1 = 0[/math] have?
  1. 0
  2. 1
  3. 2
  4. more than 2
5. 
What is the value of the discriminant of the equation [math]x^2 - 3x + 4 = 0?[/math] Then, use the value to determine whether the equation has two real solutions, one real solution, or no real solutions (two imaginary solutions).
  1. 0; one real solution
  2. -7; no real solution
  3. 9; two real solutions
  4. 8; two imaginary solutions
6. 
What is the vertex of the following function?
[math]y=2(x-4)^2+3[/math]
  1. (4,3)
  2. (4,-3)
  3. (8,6)
  4. (-4,3)
7. 
Determine the vertex form of [math]y = x^2 + 8x + 10[/math].
  1. [math]y = (x + 4)^2 + 10[/math]
  2. [math]y = (x + 4)^2 - 6[/math]
  3. [math]y = (x + 4)^2 + 26[/math]
  4. [math]y = (x - 4)^2 - 6[/math]
8. 
What is the the axis of symmetry of the quadratic equation [math]y=4x^2+6x-12 ?[/math]
  1. [math]x=-12[/math]
  2. [math]x=1/2[/math]
  3. [math]x=3/4[/math]
  4. [math]x=-3/4[/math]
9. 
What is the axis of symmetry of the following equation?
[math]y= (x-1)(x+5)[/math]
  1. x = -2
  2. x = 1
  3. x = -5
  4. x = 2
10. 
Factor the following expression:

[math]x^2 - x - 6[/math]



11. 
Factor.
[math]3x^2+13x-10[/math]



12. 
Factor. [math]9m^2 -16[/math]
  1. [math](3m-4)(3m-2)[/math]
  2. [math](3m-8)(3m+2)[/math]
  3. [math](3m-4)(3m+4)[/math]
  4. [math](3m-4)(3m-4)[/math]
13. 
Solve the quadratic equation: [math]x^2 - 4x + 4 = 0[/math]



14. 
Find the exact solutions to [math]x^2 - 3x + 1 = 0[/math] by using the Quadratic Formula.
  1. [math][-3+-sqrt(5)]/2[/math]
  2. [math][3+-sqrt(13)]/2[/math]
  3. [math][-3+-sqrt(13)]/2[/math]
  4. [math][3+-sqrt(5)]/2[/math]
15. 
Solve the equation.

[math]21x^2-7x = 0[/math]



16. 
What is the y-intercept of the quadratic equation [math]y=3x^2+2x-5[/math] ?
  1. (3,2)
  2. (0,-5)
  3. (0,5)
  4. (-3,-2)
17. 
What are the x-intercepts of the graph of [math]-x^2 +3x - 2 = 0 ?[/math]
  1. x = -1, x = -2
  2. x = 1, x = 2
  3. x = 1, x = -2
  4. x = -1, x = 2
18. 
Graph the following equation. Label the axis of symmetry, vertex, and roots (if applicable).
[math] y = 4x^2+4x-3[/math]
Graph 10x10



19. 
[math]4x^2+mx+1=0[/math] has equal roots. Hence the value(s) of m will be                   .
  1. [math] 2 [/math]
  2. [math] -2 [/math]
  3. [math]+-4[/math]
  4. [math] 16 [/math]
20. 
For the quadratic function [math]y = -2x^2-12x-10[/math]:
a. Transform the equation to the form [math]y-k=a(x-h)^2[/math]
b. Find the vertex
c. Find the x and y-intercepts
d. Sketch the graph
Graph 10x10










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