Free Printable Quadratics Test

1.

Find the axis of symmetry for
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

2.

For the quadratic y = -x² - 4x + 5, What is the y-intercept?

a)

(0, 5)

b)

(5, 0)

c)

(-2, 9)

d)

(-5, 1)

3.

The discriminant is

a)

ax² + bx + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

4.

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

5.

____________

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

a)

Positive

b)

Negative

c)

Zero

6.

Factor:

x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

7.

Solve by factoring: 4x² + 11x - 3 = 0

a)

x = -3/4 and x = -1

b)

x = 4 and x = 3

c)

x = 1/4 and x = -3

d)

x = -1/4 and x = 3

8.

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

9.

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

10.

Use the quadratic formula to solve. $4x^{2\ }+7x-15=0$

a)

x= 1.25

b)

x= 289

c)

x= 1.25, 3

d)

x= 1.25, -3

11.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

12.

Solve the following equation by completing the square:
n² - 2n - 3 = 0

a)

{3 and-1}

b)

{4 and -4}

c)

{5 and -3}

d)

{8 and -7}

13.

Solve the following equation by completing the square and write the solution in simplest radical form.
$3x^2-6x=11$

a)

$\frac{-3\pm\sqrt{42}}{3}$

b)

$\frac{6\pm\sqrt{168}}{6}$

c)

$\frac{6\pm2\sqrt{42}}{6}$

d)

$\frac{3\pm\sqrt{42}}{3}$

14.

Write the equation of the quadratic

whose roots are -4, -2.

a)

x²-6x+8

b)

x²+6x+8

c)

x²-4x-2

d)

x²-2x-4

15.

Write the equation of the quadratic

whose roots are 5/2 and 7/3.

a)

x²- 12x + 35

b)

6x²- 29x + 35

c)

6x²+ x + 35

d)

x²- x - 35

16.

Write a quadratic equation that has the roots of $x=3\pm\sqrt{2}$

a)

$y=x^2+3x+2$

b)

$y=x^2-6x+9$

c)

$y=x^2-6x+7$

d)

$y=x^2+6x+11$

17.

Write a quadratic equation that has the roots of $x=-4\pm6i$

a)

$y=x^2-10x+32$

b)

$y=x^2+8x+52$

c)

$y=x^2+8x-20$

d)

$y=x^2+8x+22$

18.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation s(t) = –16t² + 64t + 80. What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

19.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4 seconds

b)

-2 seconds

c)

-6 seconds

d)

9 seconds

20.

Find two consecutive positive integers such that the first number squared is 25 more than 3 times the second.

a)

4 and 5

b)

7 and 8

c)

-4 and -5

d)

-4 and -3

Quadratics Test

Total questions: 20

Worksheet time: 5hrs 0mins

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