Quadratic Functions

Quadratic Functions

100

What is the equation of a quadratic function? 

f(x) = ax² + bx + c

200

What is the degree of quadratic functions? 

2

300

What is the range of the following function: 

f(x) = 2x² + 4x - 4

y  ≥ -6

400

What is the interval the following function is increasing: 

f(x) = -x² + 4x + 6

x < 2

500

What are the zeroes of the following quadratic function: 

y = x² + 4x - 12

x = -6, x = 2

Quadratic Functions 2

100

Does a quadratic function that has a negative coefficient have a maximum or minimum? 

Maximum

200

Find the vertex and if it has a maximum/minimum of the following function: 

y = -x² + 2x + 8

Vertex: (1,9)

Maximum

300

Does a quadratic function that has a positive coefficient have a maximum or minimum? 

Minimum

400

Determine if the following has a maximum/minimum and find the coordinates: 

y = 5x² - 10x + 13

Minimum, (1,8) 

500

The height of an object that is traveling through the air can be modeled by a quadratic function that opens downward. The height of the object above the ground in feet is given by:

y = -16x² + 64x + 80

At what time does it hit the ground? 

5 seconds 

Axis of Symmetry

100

What is the axis of symmetry of the following equation using the graph? 

y = 2x² + 8x + 5

x = -2

200

Use the axis of symmetry formula to find the axis of symmetry of the following equation: 

y = x² + 2x + 8

x = -2

300

A quadratic function has one zero at x = -6 and a turning point at (7, 12). What is the x-coordinate of the other zero? 

x = 20

400

A quadratic function, y = (1/8)(x-2)²-8 has zeros at x=-6 and x=10. What is the coordinate of its turning point? 

(2, -8)

500

Use the axis of symmetry formula to find the axis of symmetry and turning point of the following equation: 

y = -4x² - 16x + 5

x = -2, (-2, 21)

Inverse Operations

100

Solve the following equation for x: 

2x - 3 = 9

x = 6

200

Solve the following equation for x: 

2x² + 5 = 55

x = ±5

300

Solve the following equation for x: 

4x² + 16 = 272

x = ± 8

400

Solve the following equation for x: 

(x-3)² = 25

x = 8, -2

500

Solve the following equation: 

5(x+7)² + 9 = 134

x = -2, -12

Random

100

Combine like terms: 

(2x + 5x² + 3 + 6x⁴) + (2 - 8x + 6x² + 2x⁴)

8x⁴ + 11x² - 6x + 5

200

Combine Like Terms: 

(3x² - 7x + 6) - (2x² + 4x - 4)

x² - 11x + 10

300

Find the product of 3x+2 and 2x² + 2x + 4. 

6x³ + 10x² + 16x + 8

400

Factor the following: 

x² + 7x + 12

(x+4)(x+3)

500

Factor the following: 

4x² - 25

(2x + 5)(2x - 5)