Quadratic Equations, Grade 9 Math
Name: ___________________
Analysis of Graphs & Factoring
*Make sure to read the directions, and show all your work for credit!
Part 1. The path of a ball in the air is described by the equation, h(t) = -16t2 +64t + 80,
where h is the height in meters, and t is time in seconds.
a) Find the axis of symmetry. _________
b) Find the vertex. _________
c) Show the table of values that includes the vertex.
d) Use the table to graph the equation. Use an appropriate scale for your graph.
e) When does the ball reach its maximum height? _________
f) What is the maximum height that the ball reaches? _________
g) How high is the ball at 3 seconds? _________
h) At what time will the ball at the same height as it was at 3 seconds? Why? _________
Part 2.
1) Y = ax2 + bx + c. Which coefficient makes the most impact on the graph of the equation,
and why?
2) What does it mean to solve for zeros of a quadratic equation? How does that show on the
graph?
Glencoe Algebra 2, Kuta Software
Part 3. Solve each quadratic equation by factoring. Show ALL your work
1) x2 -4x -12 = 0
5) 10x2 = 9x
2) x2 + 12x = -36
6) 2 x2 +17x + 21 = 0
3) 5 x2 -35x + 60 = 0
7) 28n4 +16n3 -80n2 = 0
4) 5p2 –p – 18 =0
8) For what values of b is the expression
factorable?
x2 + bx + 12
9) Find two consecutive even positive
integers whose product is 624.
10) Chelsea was looking through an old
algebra book and came across this
equation. The sign in front of the 6
was blotted out. How does the
missing sign depend on the signs of
the roots?
X2 6x + 8 = 0
Glencoe Algebra 2, Kuta Software
1) When Daisy shines her flashlight on the wall at a certain angle, the edge of the lit area is in the
shape of a parabola. The equation of the parabola is y = 2x2 + 2x – 60. Factor this quadratic
equation.
2) A computer graphics animator would like to make a realistic simulation of tossed ball. The
animator wants the ball to follow the parabolic trajectory represented by quadratic equation f(x) = 0.2 ( x+5) (x-5).
a) What are the solutions of f(x) = 0?
b) Write f(x) in standard form.
Glencoe Algebra 2, Kuta Software
c) If the animator changes the equation to f(x) = -0.2x2 + 20, what are the solutions of f(x) = 0?
11) A math center charges $400 for a course, and they get 750 students. For every $25 increase in
price, they lose 30 students. What price would maximize revenue?
http://imgkid.com/quadratic-formula-word-problem-examples.shtml
Glencoe Algebra 2, Kuta Software
Karen’s rectangular flower bed measures 10m by 15 m in size. She plans on doubling its area by
adding a strip of uniform width around the flower bed. A) Determine the width of the strip. B) Determine
the new dimensions with the strip. (Try this on your own, and if you need help with this, there’s a hint on
the website.)
3) What does it mean by finding the solution here? Give an explanation using the concept of solving
a quadratic equation by graphing. (You do not need to solve for x here, just give an explanation.)
0 = 3x2 + 5x – 9
Glencoe Algebra 2, Kuta Software
Glencoe Algebra 2, Kuta Software
1) What does it mean by finding the solution here? Give an explanation using the concept of solving
a quadratic equation by graphing. (You do not need to solve for x here, just give an explanation.)
0 = 3x2 + 5x – 9
Glencoe Algebra 2, Kuta Software