Investigating the Graph of y=a(x-p)2 + q
Learning Goal: In this investigation we are going to learn how the values of
a, p and q change the graph of a quadratic in vertex form.
I.
II.
Open the sketch titled graphingquadratics.gsp
Using the selection arrow, click on the + button to adjust the value of p to +5.
Q1: What happens to the parabola when you increase the value of p?
Q2: State the equation of the relation and the coordinates of the vertex.
III.
Using the selection arrow, click on the – button to adjust the value of p to –3.
Q3: What happens to the parabola when you decrease the value of p?
Q4: State the equationof the relation and the coordinates of the vertex.
IV.
Now adjust the value of p to +2 and q to +3.
Q5: What happens to the parabola when you increase q?
Q6: State the equation of the relation and the coordinates of the vertex.
V.
Now adjust the value of p to +4 and q to –5.
Q7: What happens to the parabola when you decrease q?
Q8: State the equation of the relation and the coordinates of the vertex.
VI.
Move the vertex to the point (-3,-4).
Q9: What is the value of p and q to accomplish this? What is the equation of the relation?
Q10: Does the parabola have a maximum or a minimum? What is it’s value?
VII.
Adjust the value of a to 0.
Q11: What happens to the parabola? What is the equation of the relation?
VIII.
Adjust a to –1.
Q12: What happens to the parabola?
Q13: Does it have a minimum or a maximum? What is it’s value?
IX.
Using the selection arrow change to page 2 in the bottom left hand corner of the screen.
X.
Using the selection arrow, adjust the a value to +4.
Q14: What are the x-intercepts of the parabola?
Q15: What are the coordinates of the vertex?
XI.
Adjust a to 3 and b to –1.
Q16: What are the x-intercepts of the parabola?
Q17: What are the coordinates of the vertex?
XII.
Adjust a to 2 and b to 6.
Q18: What are the x-intercepts of the parabola?
Q19: What are the coordinates of the vertex?
Q20: What is the relationship between the values of a and b and the location of the vertex?
Summary
How does it affect the graph
of y=x2 when…
a>0
(a is greater than 1)
0< a < 1 (a between 0 and 1)
-1 < a < 0 (a between -1 and 0)
a < -1 (a is less than -1)
p > 0 (p is positive)
p < 0 (p is negative)
q > 0 (q is positive)
q < 0 (q is negative)
Practice: pg 123 # 10
Affect