Graphing Quadratic Functions Worksheet

Graphing Quadratic Functions Worksheet
  • Page 1
 1.  
Katie says without drawing the graph of y = - 2x2 + 4, we can find out if its vertex is above or below the point (0, 0). Is she correct?
a.
No
b.
Yes


Solution:

Yes, Katie is correct.
It is possible to predict without drawing the graph of y = - 2x2 + 4, if its vertex would be above or below the point (0, 0).

For y = - 2x2 + 4, a = - 2, b = 0 and c = 4.
[Compare with y = ax2 + bx + c.]

Consider y = ax2 + c:
If c is positive, then the vertex of the graph of y = ax2 + c will be c units above the point (0, 0).
If c is negative, then the vertex of the graph of y = ax2 + c will be c units below the point (0, 0).

Here we have c = 4. So, the vertex of the graph of y = - 2x2 + 4 will be 4 units above the point (0, 0).


Correct answer : (2)
 2.  
Identify the list that shows all the possible rational roots of the equation 4x13 + 4x7 + 2x + 5 = 0.
a.
± 12, ± 14, ± 52, ± 54
b.
± 1, ± 12, ± 14 , ± 5
c.
± 1, ± 12, ± 14, ± 5, ± 52, ± 54
d.
± 1, ± 5


Solution:

Constant term = 5

Factors of 5 are ± 1 and ± 5.

Leading coefficient = 4

Factors of 4 are ± 1, ± 2, and 4.

Rational root = an integral factor of the constantan integral factor of the leading coefficient = ± 1, ± 12, ± 14, ± 5, ± 52, ± 54


Correct answer : (3)
 3.  
At how many points does the graph of y = x2 - 3x - 40 intersect the x-axis?
a.
one
b.
two
c.
three
d.
zero


Solution:

The graph of y = x2 - 3x - 40 intersect the x-axis at y = 0

For y = 0, x = 8 and - 5
[Substitute y = 0 in y = x2 - 3x - 40 and solve for x.]

Therefore, the points at which the graph intersect the x-axis are (8, 0) and (- 5, 0).

So, the graph intersects the x-axis at two points.


Correct answer : (2)
 4.  
At how many points does the graph of y = x2 - 2x + 1 intersect the x-axis?
a.
zero
b.
two
c.
cannot be determined
d.
one


Answer: (d)


Correct answer : (4)
 5.  
At how many points does the graph of y = x2 + 2x + 3 intersect the x-axis?
a.
cannot be determined
b.
two
c.
one
d.
zero


Answer: (d)


Correct answer : (4)
 6.  
At how many points does the graph of y = x2 - 12x + 36 intersect the x-axis?
a.
cannot be determined
b.
zero
c.
two
d.
one


Answer: (d)


Correct answer : (4)
 7.  
At how many points does the graph of y = x2 - 4x - 5 intersect the x-axis?
a.
two
b.
cannot be determined
c.
one
d.
zero


Answer: (a)


Correct answer : (1)
 8.  
At how many points does the graph of y = 2x2 - 5x - 25 intersect the x-axis?
a.
zero
b.
two
c.
cannot be determined
d.
one


Answer: (b)


Correct answer : (2)
 9.  
At how many points does the graph of y = x2 - 3x - 4 intersect the x-axis?
a.
zero
b.
one
c.
two
d.
cannot be determined


Answer: (c)


Correct answer : (3)
 10.  
What is the effect of the constant factor on the slope of the functions y1 = 5x2 - 2x + 11 and y2 = x2 - 25x + 11 5?
a.
cannot be determined
b.
no change
c.
more steeper
d.
less steeper


Answer: (d)


Correct answer : (4)

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