FINDING THE VERTEX OF A PARABOLA IN STANDARD FORM WORKSHEET

Name a, b and c for each parabola. Then find the vertex. Show all work.

Problem 1 :

f(x) = x² - 8x + 17

Solution

Problem 2 :

f(x) = -x² - 2x - 2

Solution

Problem 3 :

f(x) = -x² + 6x - 8

Solution

Problem 4 :

f(x) = -3x² + 6x

Solution

Problem 5 :

f(x) = -2x² - 16x - 31

Solution

Problem 6 :

f(x) = -1/2x² - 4x - 6

Solution

Problem 7 :

f(x) = -2x² + 12x - 22

Solution

Problem 8 :

f(x) = x² - 8x + 20

Solution

Complete the square to convert the standard form quadratic function into vertex form. Then find the vertex.

Problem 1 :

f(x) = x² + 4x - 14

Solution

Problem 2 :

f(x) = 2x² + 9x

Solution

Problem 3 :

f(x) = 5x² - 4x + 1

Solution

Problem 4 :

f(x) = x² - 16x + 70

Solution

Problem 5 :

f(x) = -3x² + 48x - 187

Solution

Example 6 :

The parabola shows the path of your first golf shot, where x is the horizontal distance (in yards) and y is the corresponding height (in yards).

The path of your second shot is modeled by the function

f(x) = −0.02x(x − 80)

Which shot travels farther before hitting the ground? Which travels higher?

Solution

Example 7 :

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

Solution

Determine the equation of quadratic function from graph. Give the function in vertex form.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Which function represents the widest parabola? Explain your reasoning.

a) y = 2(x + 3)²        b)  y = x² − 5     c)  y = 0.5(x − 1)² + 1      d)  y = −x² + 6

Solution

Problem 6 :

The graph of which function has the same axis of symmetry as the graph of

y = x² + 2x + 2?

a) y = 2x² + 2x + 2       b)  y = −3x²− 6x + 2

c)  y = x² − 2x + 2       d)  y = −5 x²+ 10x + 2

Solution

Problem 7 :

The path of a diver is modeled by the function

f(x) = −9x² + 9x + 1

where f(x) is the height of the diver (in meters) above the water and x is the horizontal distance (in meters) from the end of the diving board.

a. What is the height of the diving board?

b. What is the maximum height of the diver?

c. Describe where the diver is ascending and where the diver is descending.

Solution

Problem 1 :

Find the equation of parabola with focus (5, 0) and vertex (5, 3).

Solution

Problem 2 :

Find the equation of parabola whose focus is at (6, 3) and the vertex (2, 3) is given by.

Solution

Problem 3 :

Find the equation of parabola whose focus is at (-2, 4) and the vertex (1, 4) is given by.

Solution

Problem 4 :

Write an equation of the parabola shown.

Solution

Problem 5 :

Write an equation of the parabola with vertex at (0, 0) and the given directrix or focus.

a)  directrix: x = −3

b)  focus: (−2, 0)

c)  focus: (0, 3/2)

Solution

Problem 6 :

Which of the following are possible coordinates of the point P in the graph shown? Explain.

a)  (-6, -1)     b)  (3, -1/4)     c)  (4, -4/9)     d) (1, 1/36)      e)  (6, -1)    f)  (2, -1/18)

Solution