FINDING VERTEX AND AXIS OF SYMMETRY OF PARABOLA WORKSHEET

Identify the vertex and the axis of symmetry of each parabola.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Graph each function. Label the vertex and the axis of symmetry.

Problem 4 :

y = x² –2x – 3

Solution

Problem 5 :

y = -3x² +12x – 8

Solution

Problem 6 :

Tell whether the function f(x) = -4x² - 24x - 19 has a minimum value or a maximum value. Then find the value.

Solution

Problem 7 :

The suspension cables between the two tower of the Mackinac bridge in Michigan forn a parabola that can be modelled by y = 0.000098x² - 0.37x + 552, where x and y are measured in feet. What is the height of the cable above the water as its lowest point ?

Solution

Problem 8 :

The function

h(t) = −16t² + 16t

represents the height (in feet) of a horse t seconds after it jumps during a steeplechase.

a. When does the horse reach its maximum height?

b. Can the horse clear a fence that is 3.5 feet tall? If so, by how much?

c. How long is the horse in the air?

Solution

Problem 9 :

a. How far from each tower shown is the lowest point of the cable?

b. How high is the road above the water?

Solution

Problem 10 :

The function shown represents the height h (in feet) of a firework t seconds after it is launched. The firework explodes at its highest point

a. When does the firework explode?

b. At what height does the firework explode?

Solution

Answer Key

1) Vertex (0, 1) and equation of axis of symmetry x = 0

2)  Vertex (3, 0) and axis of symmetry at x = 3.

3)  Vertex is (0, -2) and axis of symmetry at x = -2.

4)  Vertex (1, -4) and axis of symmetry at x = 1

5) Vertex (2, 4) and axis of symmetry at x = 2

6) the maximum is at (-3, 17).

7) The cable is about 203 feet above the water at its lowest point.

8) a)  Maximum height = 4 ft

b) Since the maximum height is 4 ft, the horse can clear the height of 3.5 ft.

c) The horse will be at air in 1 second.

9) a) 200 ft is the lowest point.

b) 50 feet

10) a) After 4 seconds the firework will explode.

b) 256 ft

Determine the equation of the axis of symmetry of :

Problem 1 :

y = x² + 4x + 1

Solution

Problem 2 :

y = 2x² - 6x + 3

Solution

Problem 3 :

y = 3x² + 4x - 1

Solution

Problem 4 :

y = -x² - 4x + 5

Solution

Problem 5 :

y = -2x² + 5x + 1

Solution

Problem 6 :

y = (1/2)x² - 10x + 2

Solution

Problem 7 :

y = (1/3)x² + 4x

Solution

Problem 8 :

y = 100x - 4x²

Solution

Problem 9 :

Tell whether the function f (x) = −4x² − 24x − 19 has a minimum value or a maximum value. Then find the value

Solution

Problem 10 :

The suspension cables between the two towers of the Mackinac Bridge in Michigan form a parabola that can be modeled by

y = 0.000098x² − 0.37x + 552

where x and y are measured in feet. What is the height of the cable above the water at its lowest point?

Solution

Problem 11 :

The function shown represents the height h (in feet) of a firework t seconds after it is launched. The firework explodes at its highest point.

a. When does the firework explode?

b. At what height does the firework explode?

Solution

Problem 12 :

The function h(t) = −16t² + 16t represents the height (in feet) of a horse t seconds after it jumps during a steeplechase.

a. When does the horse reach its maximum height?

b. Can the horse clear a fence that is 3.5 feet tall? If so, by how much?

c. How long is the horse in the air?

Solution

Related Pages

• Find vertex and axis of symmetry of parabola from graph
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• Equation of parabola from three points