Vertex Form of Quadratic Relations - Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
1. Use finite differences to determine the type of relation between x and y.
x
y
5
–1
4
1
3
3
2
5
1
7
a. linear
c. neither linear nor quadratic
b. quadratic
d. unable to determine
2. Use finite differences to determine the type of relationship between x and y.
x
y
–3
3
–2
4
–1
7
0
12
1
19
a. linear
b. quadratic
3. The graph of the quadratic relation
For what value or values of x is
a.
b.
____
c. neither linear nor quadratic
d. unable to determine
is shown below.
?
c.
d.
4. Which of the following parabolas is congruent to
a.
c.
b.
d.
?
____
5. Which one of the following graphs best represents the equation
a.
c.
b.
____
d.
6. Which one of the following graphs represents the equation
a.
c.
b.
?
?
d.
____
7. What transformation must you apply to the graph of
in order to draw the graph of
a. reflection on the x-axis
c. translation 3 units to the left
b. translation 3 units downward
d. translation 3 units to the right
____
8. What transformation must you apply to the graph of
?
a. reflection on the x-axis
b. translation 3 units downward
in order to draw the graph of
c. translation 3 units to the left
d. translation 3 units to the right
?
____
9. The graph of
is vertically compressed by a factor of
a.
c.
b.
d.
____ 10. A parabola has a vertex of
and passes through the point
equations represents this parabola?
a.
c.
b.
d.
11. For the quadratic relation
a) the direction of opening
b) the stretch or compression factor
c) the coordinates of the vertex
d) the equation of the axis of symmetry
e) the maximum or minimum value of y
12.
. The equation for this new graph is
. Which one of the following
, state the following:
A railway bridge over a road is in the shape of a parabola, and the bridge is 3 m high in the middle and 6
m wide at its base. A truck that is 2 m wide is approaching the bridge. What is the maximum height that
the truck can have and still pass under the bridge? Explain your reasoning.
13. The Smith Gate is a parabolic arch that is approximately 20 m tall and approximately 22 m wide.
a) Sketch the graph
b) Determine an equation to model the arch.
14. An arrow is fired from 1.5m above the ground and reaches a maximum height of 13.5 m at a horizontal
distance of 3 m.( Hint: Draw a rough sketch). Determine an equation to model the path of the arrow.
15. Determine the equation of the given parabola.
Answer Section
1.
5.
9.
11.
ANS: A
ANS: B
ANS: C
a) upward
2. ANS: B
3. ANS: D
6. ANS: B
7. ANS: D
10. ANS: D
b) compression by a factor of 0.5
e) minimum value of –5
12. Answers will vary.
The bridge can be modelled by the equation
and the parabola opens downward. The point
the parabola is
the point where
4. ANS: C
8. ANS: C
c)
d)
if the origin is placed at the top centre of the bridge
is on the curve, therefore
and the equation of
. If the truck is centred under the bridge, one top corner of the truck will be at
. At this point is
, so the truck must have a height of less than
approximately 2.67 m.
The maximum height of the truck (assuming you are only driving down the right side) is 1.32 m.
13. a)
20
b) 𝑦 = − 121 (𝑥 − 7)2 + 20
4
14. ℎ = − 3 (𝑡 − 3)2 + 13.5
1
15. 𝑦 = 2 (𝑥 + 2)2 − 4
, or