MATH 0120
Problems in support of Waner & Costenoble, Section 9.1
The general form of the quadratic function is f ( x)  ax2  bx  c , with a, b and c representing
fixed numbers and a  0 . The graph of this function is a parabola.
1. For problem 1: f ( x)  x2  4 x  3 .
a. For this function, what are a, b, and c?
b. Fill in the values of f ( x) in the following table.
x
f ( x)
1
0
1
1.5
2
2.5
3
4
5
c. Plot the points from the table on the graph and draw the graph.
d. Let V  ( xv , yv ) represent the vertex, the point where the parabola turns around.
xv  
b
 b 
and yv  f ( xv )  f   
2a
 2a 
Find the coordinates of the vertex.
b
on the graph above. Notice that the parabola is symmetric
2a
about this vertical line through the vertex.
e. Draw the vertical line x  
f. Is a positive or negative? Which way does the parabola open? Is the y-coordinate of the
vertex a maximum or minimum value of f ( x) ?
g. What is the y-intercept of the graph?
h. What are the x-intercepts of the graph?
i. How do you calculate the y-intercept from the equation?
j. How do you find the x-intercepts (if any) from the equation?
k. What is the quadratic formula?
l. For the equation f ( x)  0  x2  4 x  3 , what is the value of the discriminant? What does that
tell you about the number of x-intercepts?
2. For problem 2: f ( x)   x2  4 x  5 .
a. For this function, what are a, b, and c?
b. Fill in the values of f ( x) in the following table.
x
f ( x)
1
0
1
1.5
2
2.5
3
4
5
c. Plot the points from the table on the graph and draw the graph.
d. Calculate the x and y coordinates of the vertex.
e. What is the value of the discriminant? What does that tell you about the number of xintercepts?
f. Is a positive or negative? Does the parabola open up or down?
g. Is the vertex above or below the x-axis? What does the location of the vertex and the direction
the parabola opens tell you about the number of x-intercepts?