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WorksheetsTopic 9 - Solving Quadratic Equations
Total questions: 20
Worksheet time: 19mins
Use the graph to find the solutions of −21x2−x+4=0
The equation ax2 + bx + c = 0 has no real solutions. Which statement about the
graph of f(x) = ax2 + bx + c could be true?
It could pass through the origin.
Its vertex could be at (−6, 0) .
It could have a maximum at (−3, 2) .
It could have a minimum at (0, 4) .
Solve the equation x2 − 2x − 3 = 0 by graphing.
x = (a) and x = (b)
(write the smaller solution on the left)
What is the factored form of the function shown in the graph?
(x + 4)(x − 1)
(x − 4)(x + 1)
(x − 4)(x − 1)
(x + 4)(x + 1)
What are the solutions of the equation
4x2 − 2x + 2 − 3x − x2 = 0 ?
1 and 2
1 and 2/3
-1 and -2
-1 and -2/3
Use factoring to find the factored form of the equation x2 + 8x + 12 = 0
Solve the equation x2 + 9x = 36 by factoring.
Select all the equations that have −4 and 4 as solutions. (Hint: there are 2 answers)
x2 = 8
x2 + 16 = 0
2x2 = 32
6x2 + 56 = -40
27 - 5x2 = -53
Which equation has no real solutions?
−2x2 = −168
4x2 + 76 = 32
25x2 = 1
43 − x2 = 12
Solve for x . Round to the nearest tenth of a foot.
x = ?
State how many real solutions each equation has.
x2 = −100 (a)
5x2 = 1 (b)
6x2 + 17 = 11 (c)
7(x2 + 6) = 42 (d)
Which value of c completes the square (aka. makes a perfect square trinomial) in the expression x2 + 14x + c ?
-49
-7
7
49
Solve x2 + 12x + 25 = 17 by completing the square. Select all the possible solutions.
−6+7
−6+27
6−27
−6−7
−6−27
The function a = −2x2 + 8x + 5 models the altitude a in feet of a ball thrown in
the air and the horizontal distance x in feet that the ball travels. Which is the
vertex form of the function?
a = −2( x − 2 )2 + 3
a = −2( x + 2 )2 − 3
a = −2( x − 2 )2 + 13
a = −2( x + 2 )2 + 13
Use the discriminant to determine how many real solutions each equation has.
8x2 − 10x + 15 = 0 (a)
2x2 − 8x − 1 = 0 (b)
− x2 + 12x − 36 = 0 (c)
Select all the statements about the graph shown that are true. (hint: there are 3 answers)
An equation for the graph is y = 2x2 − 9x + 7 .
The function has two roots.
The solutions of the related quadratic equation are −1.5 and −3 .
The related quadratic equation has two solutions.
The discriminant of the related quadratic equation is negative.
The profit P , in dollars, of a small business can be modeled by the function P(x) = 0.3x2 + 7x − 40 , where x is the number of units sold. How many units need to be sold for the business to make a profit of $60?
What is a solution of the system of equations shown?
(−4, 0)
(2, −4)
(0, −2)
(2, 0)
Use elimination to solve the system of equations.
y = x2 − 3x + 16
y = 9x − 20
Use substitution to solve the system of equations.
y = x2 − 7x − 5
y = −2x + 19
( (a) , (b) ) and ( (c) , (d) )
(NOTE: Write the coordinate with the bigger x value FIRST)
