Lesson 10.1 • Solving Quadratic Equations Name

Period

Date

1. Sketch the graph of a quadratic equation with each set of conditions. a. One x-intercept and all nonnegative y-values b. The vertex in the third quadrant and no x-intercepts c. The vertex in the third quadrant and two x-intercepts d. The vertex on the y-axis and two x-intercepts, opening upward 2. Use a graph to find the number of solutions for each function. a. 0 ! 4(x " 3)2 # 5

b. 0 ! #4(x " 3)2 # 5

c. 0 ! (x " 5)2

d. 0 ! 3(x # 1)2 " 1

e. 0 ! x 2 # 8x " 16

f. 0 ! x 2 # 4x " 2

g. 0 ! #3x 2 # 6x " 11

h. 0 ! #3x 2 # 6x # 11

i. 0 ! x 2 " 8x " 16 3. For each equation, find the solutions to the nearest hundredth by

zooming in on a table or graph. a. 0 ! x 2 " x " 1

b. 0 ! x 2 # 5x " 3

c. 0 ! 2x 2 # 13x " 9

d. 0 ! 7x 2 #10x # 3

e. 0 ! 2(x " 5)2 # 3

f. 0 ! 0.5(x # 3)2 " 2

4. Use a symbolic method to solve each equation. Show each solution

exactly as a radical expression. a. x 2 ! 21

b. x 2 # 5 ! 18

c. 2(x " 1)2 # 4 ! 10

d. x 2 " 16 ! 0

e. x 2 # 13 ! 27

f. $$ x " $$

1 6

!

1 2

" " $34$ ! $94$ 2

5. Given the two functions f(x) ! x 2 # 4x " 5 and g(x) ! 3x 2 " 2x # 1,

find each answer without a calculator.

66

! 12 "

a. f(2)

b. f(3)

c. f $$

e. g(#2)

f. g(0)

g. g(2)

Discovering Algebra More Practice Your Skills

! 12 " 1 h. g !$$" 2 d. f #$$

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