Quadratics review

Factoring

100

Factor the function: 

f(x) = x² - 9x + 20

What is...

f(x) = (x-4)(x-5)

200

Factor the function:

f(x)= x²-16x+64

What is...

f(x)= (x-8)²

300

Factor the function:

f(x) = 4x²-36x+81

What is...

f(x)=(2x-9)²

400

Factor the function:

f(x)=-2x²-13x+15

What is...

f(x)= (-2x-15)(x-1)

500

Factor the function:

f(x)=x²+4x-17

What is...

f(x)=(x-2.58)(x+6.58)

Properties of parabolas

100

Does this parabola open up or down?

f(x)= -3x²-4x+12

What is...

Opens down

200

Does this parabola have a maximum or minimum point?

f(x)= 5x²+9x-20

What is...

A minimum point.

300

What are the x-intercept(s) of the function

f(x) = x² - 2x + 1

What is...

(1,0)

400

What is the axis of symmetry of this functions parabola?

f(x)= -3x²+8x

What is...

x=4/3

500

What is the vertex point of this functions parabola?

f(x)= -2x²+3x+9

What is...

(3/4, 81/8) 

(0.75, 10.125)

Complex numbers

100

What is the value of i⁵⁴?

What is...

i² = -1

200

Evaluate:

(4+3i) - (5-6i)

What is...

-1+9i

300

Evaluate:

(3-2i)(-6+4i)

What is...

-10+24i

400

Evaluate: 

(2+i)/(3i) 

What is...

(-2i+1)/(3)

500

Evaluate: 

(5+4i)/(3-2i)

What is...

(7+22i)/(13)

Solving using any method

100

What are the solution(s) of this equation:

9x²+81x=0

What is...

x=0, x= -9

200

What are the solution(s) of this equation:

x²-3x-10=0

What is...

x=-2, x=5 

300

What are the solution(s) of this equation:

4x²+121=0

What is...

x = (11/2)i, x = -(11/2)i

400

What are the solution(s) of this equation:

10x²+25x=15

What is...

x= -3, x = (1/2)

500

What are the solution(s) of this equation:

15x²-84x-36=0

What is...

x = (-2/5), x = 6

Quadratic formula

100

What does b²-4ac from the Quadratic Formula tell you about an equations solutions. 

What is...

The discriminant: the # of solutions and the type. 

200

Find the axis of symmetry of the function below using the Quadratic Formula:

f(x)=x²-15x+47

What is...

x= 15/2

300

What is the discriminant of the equation below and how many solutions and what type of solutions does it have?

7x²-11x+5=0

What is...

D=-19, 2 complex roots 

400

What is the discriminant of the equation below and how many solutions and what type of solutions does it have?

x²+22x+121=0

What is...

D=0, one real root 

500

Solve the equation below using the Quadratic Formula:

3x²-4x-8=-6

What is...

x=(2/3)+(square root of 10 /3)

x=(2/3)-(square root of 10 /3)