REVIEW ON QUADRATIC EQUATION AND FUNCTIONS

Problem 1 :

Write an equation for the parabola whose vertex is at (3, 6) and which passes through (4, 4).

a. y = -2(x + 3)² – 6                    c. y = 2(x - 3)² + 6

b. y = (x + 3)² – 6                        d. y = -2(x - 3)² + 6 

Solution

Problem 2 :

Solve the quadratic equation :

x² + 10x + 22 = 0

a. 5 ± 2√7        c.100 ± √3

b. -5 ± √3        d.-10 ± 2√7

Solution

Problem 3 :

The function y = -16t² + 248 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground ? Round to the nearest hundredth of a second.

a. 7.87 seconds       c. 3.94 seconds

b. 0.25 seconds        d. 5.57 seconds

Solution

Problem 4 :

Use a graphing calculator to solve the equation -10x² – 2x + 3 = 0. If necessary, round to the nearest hundredth.

a. – 0.46, 0.66       c. -0.66, 0.46

b. -1.31, 0.91         d. -0.56, 0.56

Solution

Problem 5 :

Solve the equation.

36x² + 4 = 0

a. -1/3i, 1/3i           c. -1/9i, 1/9i

b.  -1/3, 1/3           d. -3i, 3i

Solution

Problem 6 :

Which is the graph of y = (x – 2)² + 4?

a)

b)

c)

d)

Solution

Problem 7 :

Solve by factoring.

4x² + 10x – 24 = 0

a.  3/2, -1        c. 4, -1

b. -4, 3/2        d. -4, 4

Solution

Problem 8 :

Identify the vertex and the y – intercept of the graph of the function y = 2(x + 2)² – 2.

a. vertex : (2, 2), y – intercept : 8 

b. vertex : (-2, -2), y – intercept : 6

c. vertex : (2, -2), y – intercept : 6

d. vertex : (-2, 2), y – intercept : 2

Solution

Problem 9 :

y = 3x² – 36x + 111. What is the minimum value of the function ?

Solution

Problem 10 :

Use vertex form to write the equation of the parabola. 

a. y = (x – 2)² – 3        c.  y = 3(x - 2)² - 3

b. y = 3(x + 2)² – 3       d. y = 3(x + 2)² + 3

Solution