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1.5 Quadratic Formula and Discriminant

Total questions: 38

Worksheet time: 2hrs 30mins

Name
Class
Date
1.
Determine the values of
a, b, and c for
the quadratic equation: 
4x2 – 8x = 3
a)
a = 4, b = -8, c = 3
b)
a = 4, b =-8, c =-3
c)
a = 4, b = 8, c = 3
d)
a = 4, b = 8, c = -3
2.
Solve    2x2 + 7x - 15 = 0
a)
-1.5 or 5
b)
No Solution
c)
-5 or 1.5
d)
0.7 or 5
3.
Solve using the quadratic formula.
2x2 - 9x - 35 = 0
a)
x = 7/2, x = -6
b)
x = -5/2, x =5
c)
x = -3/7, x =6
d)
x = -5/2, x = 7
4.
Identify the 'b' value: y = 16x2 -8x -24
a)
16
b)
-8
c)
8
d)
-24
5.
What should you do first in solving this equation?
x2 + 6x - 13 = 3
a)
Get factored form
b)
Write down: a=1, b=6, c=-13
c)
Make it equal 0 by subtracting 3 on each side
d)
Type it all in a calculator.
6.

The discriminant is

a)

ax2 + bx + c

b)

b - 4ac

c)

b2 - 4ac

d)

b2 + 4ac

7.

If the discriminant equals 0, then the quadratic has:

a)

1 Rational Solution

b)

2 Rational Solutions

c)

No solutions

d)

2 Complex Solutions

8.

5x2+3x−3=05x^2+3x-3=0  

a)

−3±i5110\frac{-3\pm i\sqrt{51}}{10}  

b)

−3±6910\frac{-3\pm\sqrt{69}}{10}  

c)

3±692\frac{3\pm\sqrt{69}}{2}  

d)

−3±32310\frac{-3\pm3\sqrt{23}}{10}  

9.

x2−6x+4=0x^2-6x+4=0  

a)

3±53\pm\sqrt{5}  

b)

6±202\frac{6\pm\sqrt{20}}{2}  

c)

3±203\pm\sqrt{20}  

d)

3±i133\pm i\sqrt{13}  

10.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

11.

What is the discriminant of -2x2 − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

12.

What is the discriminant of 6x2 − 2x − 3 = 0

a)

76

b)

29

c)

68

d)

none of these

13.

What is the discriminant for 5x2 + x − 2 = 0

a)

-39

b)

42

c)

-41

d)

none of these

14.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

15.
A function has a discriminant of 25.
______________
How many solutions does it have?
a)
0
b)
1
c)
2
d)
5
16.
A function has a discriminant of -3.
______________
How many x-intercepts does it have?
a)
0
b)
1
c)
2
d)
3
17.
What  are the solutions of this graph?
a)
-2 and 3
b)
-1/2 and -6
c)
-2 and -6
d)
3 and -6
18.

How many solutions will this quadratic equation x2+8x+16 has?

a)

2 real solutions

b)

2 imaginary solution

c)

1 solution

d)

3 solutions

19.

Determine the values of a, b, and c for the quadratic equation:

4x2 – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

20.

Use the quadratic formula to solve 2x2 + 2x - 12.

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

21.
Determine the values of
a, b, and c for
the quadratic equation: 
4x2 – 8x = 3
*remember right side should =0
a)
a = 4, b = -8, c = 3
b)
a = 4, b =-8, c =-3
c)
a = 4, b = 8, c = 3
d)
a = 4, b = 8, c = -3
22.

What should you do first in solving this equation?

x2 + 6x - 13 = 3

a)

Factor

b)

Write down: a = 1, b = 6, c = -13

c)

Subtract 3 from both sides.

d)

Add 3 to both sides.

23.
The discriminant is
a)
aX2  + bX  +  c
b)
b - 4ac
c)
b2 - 4ac
d)
b2 + 4ac
24.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

25.

What is the discriminant of -2x2 − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

26.
What is the name of this property?
a)
Zero Exponent Property
b)
Zero Product Property
c)
Commutative Property
d)
Zero Sum Property
27.

Use the quadratic formula to find the solutions for

y = -x2 - 5x + 12

a)

No Real Solution

b)
c)
d)
28.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

29.
A function has a discriminant of 25.
______________
How many solutions does it have?
a)
0
b)
1
c)
2
d)
5
30.
A function has a discriminant of -3.
______________
How many x-intercepts does it have?
a)
0
b)
1
c)
2
d)
3
31.
____________
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
32.
Find the zeros of the equation: 
(x+10)(x-2) = 0
a)
10 and 2
b)
-2 and 10
c)
-10 and 2
d)
-2 and -10
33.
____________
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
34.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

35.
What  are the solutions of this graph?
a)
-2 and 3
b)
-1/2 and -6
c)
-2 and -6
d)
3 and -6
36.

Given the equation 10x2 -6x=0, what is the value of C?

a)

0

b)

-6

c)

10

d)

x

37.

Write this equation x2 -6 = x in standard form.

a)

x2 +6x=0

b)

x2 -6x=0

c)

x2 -x -6 =0

d)

x2 +x -6

38.

Which equation is the standard form of a quadratic function?

a)

f(x) = mx + b

b)

f(x) = a(x - m)(x - n)

c)

f(x) = ax2 + bx + c

d)

f(x) = a(x - h)2 + k

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