MATH HIGH SCHOOL
QUADRATIC EQUATIONS
EXERCISES
High School: Quadratic Equations
LESSON 3: FACTORED FORM
EXERCISES
EXERCISES
y
1.
6
4
2
–5
x
5
–2
–4
–6
–8
Fill in the equation for this parabola in factored form.
y = (x – )(x – )
A –6, –2, –3
B 1, –2, 3
C 0.5, 1, 2
D –1, 2, 3
y
2.
6
4
2
–10 –8 –6 –4 –2
–2
2
4
6
8 10 x
–4
–6
–8
Fill in the equation for this parabola in standard form.
y = x2 + x +
A 3, 1, –6
B 1, 0.5, –1
C 2, –1, 3
D 1, –1, –6
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High School: Quadratic Equations
LESSON 3: FACTORED FORM
3.
EXERCISES
What do you need to write this quadratic equation in factored form:
y = x 2 + 9 x + 14
A The product of 9 and 14 divided by 2
B The sum of the coefficients 1, 9, 14 divided by 3
C Two numbers that multiply to 14 and add up to 9
D Two numbers that multiply to 9 and that add up to 14
4. Write this quadratic equation in factored form.
f ( x ) = x 2 + 7 x − 44
(
f (x) = x +
5.
)(x −
)
f(x) = (2x + 3)(x – 4)
Explain how does the factored form of a quadratic equation relate to the graph.
6. Write this quadratic equation in factored form:
y = 2 x 2 − 16 x + 32
7.
Write this quadratic equation in factored form.
y = 3x 2 − x − 2
8. Select all expressions that represent a factorization of x 2 − 12 x + 32
A
B
C
D
E
9.
( x − 3) ( x + 12 )
(8 − x ) (4 − x )
(−x + 8) (−x + 4)
( x − 2 ) ( x + 16 )
( x − 8) ( x − 4)
3 x 2 − 48
Factor this expression.
Fill in the blanks for the completely factored expressions.
(x + )(x − )
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High School: Quadratic Equations
LESSON 3: FACTORED FORM
EXERCISES
2
10. 3 x − 48
What are the zeros for the quadratic function that the expression defines?
x=
and x =
Challenge Problem
11. What can you say about the graph of a quadratic with the form y = a ( x − b ) ?
Explain.
2
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MATH HIGH SCHOOL
QUADRATIC EQUATIONS
ANSWERS
FOR EXERCISES
High School: Quadratic Equations
LESSON 3: FACTORED FORM
ANSWERS
ANSWERS
A.APR.3 1.
B
A.SSE.3.a 2.
A.APR.3
D 1, –1, –6
A.SSE.3.a 3.
C
A.SSE.3.a 4.
A.APR.3
f ( x ) = ( x + 11) ( x − 4 )
A.SSE.3.a 5.
A.APR.3
The factored form shows the zeros or x-intercepts of the function. For this function,
2
the zeros are 4 and – .
3
A.SSE.3.a 6.
A.APR.3
y = 2 ( x − 4)
A.SSE.3.a 7.
A.APR.3
y = ( 3 x + 2 ) ( x − 1)
A.SSE.3.a 8.
B
1, –2, 3
Two numbers that multiply to 14 and add up to 9
2
C
E
(8 − x ) (4 − x )
(−x + 8) (−x + 4)
( x − 8) ( x − 4)
A.SSE.3.a 9.
y = 3( x + 4) ( x − 4)
A.SSE.3.a 10.
A.APR.3
x = 4 and x = –4
Challenge Problem
A.APR.3 11.
The graph has just one real root, b. This means the quadratic touches the x-axis at
just one point, and must therefore have the vertex (b, 0).
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