1. The document provides examples of solving quadratic equations by identifying them, using the quadratic formula, factoring, and graphing. 2. Key steps covered include identifying the standard form of a quadratic equation, using the quadratic formula, finding roots by setting factored expressions equal to 0, graphing translations and intersections of quadratics, and factoring quadratic expressions. 3. Examples are worked through demonstrating these techniques for solving quadratics.

1. Quadratic Graphing Roots of Factoring
Equations Quadratics Quadratics Quadratics
1 point 1 point 1 point 1 point
2 points 2 points 2 points 2 points
3 points 3 points 3 points 3 points

2. Identify the equation below that is a quadratic
equation.
A. 4x3 + 2x2 + 7x + 4 B. x2 + 8x - 16
C. (x2 + y2) – 4 = 0 D. x3 + 2x + 5

3. 2 ± sqrt( 4 + 24)) is which equation written in the
2 quadratic formula?
A. 2x2 + 2x – 6 B. x2 – 2x - 6
C. x2 + 2x – 6 D. x2 + 2x + 6

4. (x – 6) = 0 and (x – 12) = 0 are the factors for
which of the following quadratic equations:
A. x2 + 18x – 72 B. x2 - 18x – 72
C. x2 + 18x + 72 D. x2 - 18x + 72

5. Identify the Graph of a Quadratic Function.
y = 2x+3 y = 5x2 +4x-4
y = x3 +2x+1 y =|3x-3|

6. Draw the graph of the translation of the quadratic
function y = x2 up 2 units and to the right 4
units.

7. Draw the Graph of y = 2x + 1 and y = x2 + 2x – 6
from -4 < x < 4 and find the place (s) they
intersect on the graph.

8. Find the coordinates of the root(s) on
the graph shown.

9. For 6x2 + 27x + 30, which has a
factorization of (3x + 6)(2x+5) = 0
what are the roots?

10. Use the quadratic formula to find
the roots of 2x2 + 7x – 13.

11. CHOOSE THE FACTORS OF THIS
QUADRATIC EQUATION
x2 + 6x + 9
A. (x + 9)(x + 7) B. (x + 3)(x + 3)
C. (x - 1)(x - 3) D. (x - 5)(x - 3)

12. CHOOSE THE FACTORS OF THIS
QUADRATIC EQUATION
x2 + -6x -16
A. (x - 8)(x + 2) B. (x - 8 )(x - 2)
C. (x + 8)(x - 2) D. (x + 8)(x + 2)


13. FACTOR:
x 2 - 10x - 75

15. Identify the equation below that is a quadratic
equation.
B. x2 + 8x – 16
A quadratic equation has the form
ax2 + bx + c where a, b and c are
numbers and at least a is non-zero

16. 2 ± sqrt( 4 + 24)) is which equation written in the
2 quadratic formula?
B. x2 – 2x – 6
x = -b ± sqrt(b2 – 4ac))
2a
General quadratic: ax2 + bx + c
2 = -b, b = -2
2a = 2, a = 1
-4ac = 24, 4c = -24, c = -6

17. (x – 6) = 0 and (x – 12) = 0 are the factors for
which of the following quadratic equations:
D. x2 - 18x + 72
(x – 6)(x – 12)
= (x)(x) – 6x – 12x + (6)(12)
= x2 – 18x + 72

18. Identify the Graph of a Quadratic Function.
y = 5x2 + 4x - 4

19. Draw the graph of the translation of the quadratic
function y = x2 up 2 units and to the right 4
units.
y = (x – 4)2 + 2

20. Draw the Graph of y = 2x + 1 and y = x2 + 2x – 6
from -4 < x < 4 and find the place (s) they
intersect on the graph.
y = x2 + 2x - 6
y = 2x +1

21. Find the coordinates of the root(s) of
the graph shown.
(0.5, 0)
(-2.5, 0)

22. For 6x2 + 27x + 30, which has a factorization of
(3x + 6)(2x+5) = 0 what are the roots?
x = -2, x = -5/2
3x + 6 = 0 2x + 5 = 0
3x = -6 2x = -5
x = -2 x = -5/2

23. Use the quadratic formula to find the
roots of 2x2 + 7x – 13.
x = [-7 ± sqrt(72 – 4(2)(-13))]/2
x = [-7 ± sqrt( 49 + 104)]/2
x = -(7/2) ± (sqrt(153)/2)
x = -3.5 ± 1.5(sqrt(17))

24. CHOOSE THE FACTORS OF THIS
QUADRATIC EQUATION
x2 + 6x + 9
B. (x + 3)(x + 3)
x2 + 3x + 3x + 9
x(x + 3) + 3(x + 3)
(x + 3)(x + 3)

25. CHOOSE THE FACTORS OF THIS
QUADRATIC EQUATION
x2 + -6x -16
A. (x - 8)(x + 2)
x2 - 8x + 2x - 16
x(x - 8) + 2(x - 8)
(x - 8)(x + 2)

26. FACTOR:
x 2 + -10x - 75
ANSWER: (x - 15)(x + 5)
x2 – 15x + 5x – 75
x(x – 15) + 5(x – 15)
(x – 15)(x + 5)