1
 A.SSE.2: I can take a quadratic expression and identify different ways to rewrite it.
 A.CED.1: I can create equations and inequalities in one variable and use them to solve
problems.
 A.APR.3: I can identify the ‘zeros’ of a quadratic function.
--Solving a quadratic function is actually finding the place or places
where the function crosses the x-axis. These x-intercepts are called
solutions, roots, or zeros of the quadratic function.
--One method used to solve a quadratic function is called factoring.
--The Zero Product Property states that if (x+p)(x+q) = 0, then x+p = 0
or x + q = 0. Therefore, once we factor a quadratic and put the quadratic
into intercept form, then we can set each factor equal to 0, and solve for
x. This x value will be the solution to the quadratic equation.
Solve each quadratic function.
1. x2 + 11x + 28=0
2. x2 + 11x + 24=0
3. s2 + 13s + 42=0
4. x2  10x + 21=0
5. x2 + 9x  18=0
6. w2 + 12w  35=0
7. 6x2  9=0
8. 16m2 + 8m=0
9. 2a2 + 22a + 60=0
10. 5x2 + 25x  70=0
11. 5x2  17x + 6=0
12. 3x2 + 10x + 8=0
13. n2  49=0
14. 2x2  50=0
2
15. The area of a rectangular field is x2  x  72 m2. The length of the field is x + 8 m.
What is the width of the field in meters?
16. The product of two integers is w2  3w  40, where w is a whole number. Write
expressions for each of the two integers in terms of w.
17. John is j years old. The product of his younger brother’s and older sister’s
ages is j2  2j  15. How old are John’s brother and sister in terms of John’s
age?
Solve each equation by factoring. Check your answers.
18. x2 – 2x – 24 = 0
19. 3x2 = x + 4
20. x2 – 6x + 9 = 0
21. 3x2 + 45 = 24x
Solve each equation using tables. Give each answer to at most two decimal
places.
22. 5x2 + 7x – 6 = 0
23. x2 – 2x = 1
Solve each equation by graphing. Give each answer to at most two decimal
places.
24. 10x2 = 4 – 3x
25. 3x2 + 2x = 2
26. A woman drops a front door key to her husband from their apartment window
several stories above the ground. The function h = –16t2 + 64 gives the height h of
the key in feet, t seconds after she releases it.
a. How long does it take the key to reach the ground?
b. What are the reasonable domain and range for the function h?
27. You use a rectangular piece of cardboard measuring 20 in. by 30 in. to construct a
box. You cut squares with sides x in. from each corner of the piece of cardboard and
then fold up the sides to form the bottom.
a. Write a function A representing the area of the base of the box in
terms of x.
b. What is a reasonable domain for the function A?
sc. Write an equation if the area of the base must be 416 in.2.
d. Solve the equation in part (c) for values of x in the reasonable domain.
e. What are the dimensions of the base of the box?
3
28. STEM: Physics: The function h = −16𝑡 2 + 1700, gives an object’s height ‘h’, in feet, at ‘t’ seconds.
a. What does the constant 1700 tell you about the height of the object?
b. What does the coefficient of 𝑡 2 tell you about the direction the object is moving?
c. When will the object be 1000 feet above the ground?
d. When will the object be 940 feet above the ground?
e. What are the reasonable domain and range for the function ‘h’?