Download Solving and Graphing Quadratic Equations

Solving and Graphing Quadratic Equations
3
1. Solve by completing the square (type simplified fraction) x 2  x  3
2
3
57
What is the solution? X=  
4
4
2. Solve 6x 4 19 x 2  15  0 (simplify the answer) the solution is
5
3
x= 
and x = 
3
2
3. Solve for x
5x 2  29 x  20
x = -5 and x = 
4
5
4. A) Solve 4x 2 25  0
b) Find the x-intercepts of fx(x) =4x 2 25
a) What are the solutions? X= no solution
b) What are the x-intercepts? No x intercept
5. A student opens a mathematics book to two facing pages. The product of the page
number is 812. Find the page numbers.
The first page is 28
The second page is 29
6. The width of a rectangle is 1ft less than the length. The area is 12ft 2 find the length
and the width.
The width is
The length is
3 ft.
4 ft.
7. Give exact and approximate solutions to three decimals places x 2 18 x  81  64
What are the exact solutions? x = -1 and x = -17
8. Graph the function. Find the vertex, line of symmetry and maximum or minimum
value.
Fx(x) = (x+5) 2 2
f(x)
35
30
25
20
15
10
5
x
0
-12
-10
-8
-6
-4
-2
-5
0
2
-10
The vertex is. (-5, -2)
The minimum value is fx(x) = -2
9. Find the vertex, the line of symmetry, the maximum or minimum value of the
quadratic function and graph the function on paper.
Fx(x) =x 2 12 x  1 = (x - 6)2 - 37
f(x)
20
10
x
0
-4
-2
0
2
4
6
8
10
-10
-20
-30
-40
What is the vertex? (6, -37)
What is the equation of the line of symmetry? X = 6
12
14
What is the maximum/minimum of f(x)? -37
Is the value f (6) = -37 a minimum or maximum? Minimum
10. Find the vertex, the line of symmetry, the maximum or minimum value of the
quadratic function and graph the function.
F(x) =2x 2 8 x  20 = 2(x - 2)2 + 12
What is the vertex? (2, 12)
What is the equation of the line of symmetry? X = 2
What is the maximum/minimum of f(x)? 12
Is the value, f (2) =12 a minimum or a maximum? Minimum
11. A) Solve x 2 7 x  11  0
b) Find the x-intercepts of f(x) =x 2 7 x  11
7
93
What are the solutions? X =  
2
2
7
93
7
93
What are the x-intercepts? (  
) and (  
)
2
2
2
2
12. Find the vertex, the line of symmetry, the maximum or minimum value of the
quadratic function and graph the function.
F(x) = 5-x 2
f(x)
6
4
2
x
0
-5
-4
-3
-2
-1
-2
0
1
2
-4
-6
-8
-10
-12
What is the vertex? (0, 5)
What is the equation of the line of symmetry? X = 0
What is the maximum/minimum of f(x)? 5
3
4
5
Is the value f (0) = 5 a minimum or maximum? Maximum
13. Find and label the vertex and the line of symmetry. Graph the function f(x) = 2x 2
The vertex is. (0, 0)
The equation of the line of symmetry is x = 0
14. Determine the nature of the solution of the equation.
x 2 - 12x + 36 = 0
What does the equation have? One real solution
15. Give exact and approximate solutions to three decimals places
(x+9) 2  49
What are the exact solutions x = -2 and x = -16
There are no approximate solutions since the solutions are integers
16, a) Solve 4x+x(x-2) =0
b) Find the x-intercepts of f(x) =4x+x(x-2)
What are the solutions? X = 0 & -2
What are the x-intercepts? (0, 0) and (-2, 0)
17. Write the quadratic equation in the variable x having the given numbers as solutions.
Type the equation in standard form ax 2 bx  c  0
The solution are -11, 5
The equation is x2 + 6x -55 = 0
18. Write a quadratic equation in the variable x having the given numbers as solutions.
Type the equation in standard form, ax 2 bx  c  0
Solution 7, only solution
The equation is x2 - 14x + 49 = 0
19. A) Solve 3x 2 5 x  13  0
b) Find the x-intercepts of f(x) = 3x 2 5 x  13
a) What are the solutions? X =
5
181

6
6
(Simplify answer)
5
181
5
181
b) What are the x-intercepts? ( 
, 0) and ( 
, 0)
6
6
6
6
20. Give exact and approximate solutions to three decimals places.
x 2 5 x  5  0
The exact solutions are. x =
5
181

6
6
The approximate solutions to 3 decimals places are x = 3.076 and x = -1.409
21. Find and label the vertex and the line of symmetry. Graph the functions
f(x) = (x+3) 2
f(x)
18
16
14
12
10
8
6
4
2
x
0
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
The vertex is. (-3, 0)
The equations of the line of symmetry are. X= -3
22. Find the vertex, the line of symmetry and the maximum or minimum value of f(x).
Graph the function.
F(x) = -5(x+8) 2 3
50
-17
-15
-13
-11
-9
-7
-5
-3
0
-1
-50
f(x)
x
1
-100
-150
-200
-250
-300
-350
-400
The vertex is. (-8, 3)
The line of symmetry is. X = -8
The maximum/minimum value of f(x) is 3
Is the value, f (-8) =3, a minimum or a maximum? Maximum
23 Determine the nature of the solutions of the equation x 2 13  0
Choose the nature of the solutions of the equations
Two imaginary solutions
24. The number of tickets sold each day for an upcoming performance of Handel’s
Messiah is given by N(x) = - 0.5x 2 14 x  12 where x is the number of days since the
concert was first announced. When will daily ticket sales peak and how many tickets will
be sold that day?
Ticket sales will peak 14 days after the concert was first announced.
The number of tickets sold on that day will be 110
(Round to the nearest integer)
25. Find the x and y-intercepts f(x) = 25x 2 20 x  4
The y-intercept is? (0, 4)
The x-intercept is? (-0.4, 0)