IB Math SL - 1
HW1 – Intro to Quadratics
Name_________________________________
Part I. Show that each function is a quadratic function by writing it in the standard form and identifying
a, b, and c.
1. f ( x)  ( x  5)( x  6)
2. g ( x)  (6 x  1)(2 x  3)
3. h( x)  (2  x)(8  5 x)
4. d ( x)  (6 x  4)(3x  1)
5. y( x)  3  x  2 x  5
6. m( x)  ( x  5) 2  3
Part II. Identify whether each function is quadratic. (yes or no)
7. f ( x)  x 2  3 x( x  2)
Part III.
8. w( x)  17  5 x
9. t ( x)  5x  x  x  4
State, by looking, whether the parabola is concave up or down and whether the vertex is
maximum or a minimum.
10. f ( x)  5 x 2  4 x
11. f ( x)  7  8 x  9 x 2
12. f ( x)  4 x  6 x 2
Part IV. Use your graphing calculator. Find the vertex, line of symmetry, max or min, and the zeros of
the following functions.
13. f ( x)  7 x 2  6 x  10
14. f ( x)  2 x 2  5 x  1
15. f ( x)  7  3x  x 2
Part V.
Write the standard form of the quadratic function that has the indicated vertex and whose
graph passes through the given point.
16. Vertex:  2,5
Part VI.
Point:
0,9
5 3
17. Vertex:  , 
2 4
Point:
 2,4
Answer the following.
18. The height y (in feet) of a ball thrown by a child is given by y  
horizontal distance (in feet) from where the ball is thrown.
a. Use a GDC to graph the path of the ball.
b. How high is the ball when it leaves the child’s hand?
c. What is the maximum height of the ball?
d. How far from the child does the ball strike the ground?
1 2
x  2 x  4 where x is the
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