Alg 2/Trig Chapter 4

State the vertex, axis of symmetry, Max or minimum, and the domain and range of y=-1.5(x+20)^2.

(-20,0), x=-20, Max is 0, All real numbers, y<=0

State the vertex, axis of symmetry, Max or minimum, and the domain and range of y=-1.5(x+20)^2.

(-20,0), x=-20, Max is 0, All real numbers, y>=0

Factor the expression: 4x^2-4x-3

(2x-3)(2x+1)

Factor each expression: x^2+22x+40

(x+20)(x+2)

Factor the trinomial of y=x^2-14x+49

(x-7)^2

Factor each expression: 5y^2+12y-32

(y+4)(5y-8)

Complete the square: x^2-x__

+1/4

Factor each expression: -x^2+5x-4

-(x-4)(x-1)

Write each quotient as a complex number: -2i/1+i

-1-i

Divide: 4-i / 6i

-1/6 - 2i/3

Solve each equation: 9x^2+24x+16=36

-10/3 or 2/3

Find all solutions to each quadratic equation: x^2+2x+3=0

-1±i sqrt2

Solve the quadratic equation by completing the square: 25x^2+30x=12

-3/5 ± sqrt 21/5

Simplify each expression: (-6i)^2

-36

Solve each equation using any method. Round real solutions to the nearest hundredth: 5x^2+8x-11=0

-4 ± sqrt 291 / 5

Solve each equation: 25x^2+10x+1=9

-4/5 or 2/5

Solve each equation using any method. Round real solutions to the nearest hundredth: x^2+8x=4

-4±s sqrt5

Solve each equation using the Quadratic Formula: x^2+10x=-25

-5

Solve each quadratic function by completing the square: x^2+5x-3=0

-5/2 ± sqrt 37/2

Solve the quadratic equation by completing the square: 4x^2+10x-3=0

-5/4 ± sqrt21/5

Solve by completing the square: x^2+10x-3=0

-5±2sqrt7

Factor each expression: -6z^2-600

-6(z^2+100)

Simplify each expression: (-6-7i) - (1+3i)

-7-10i

Solve each equation by factoring: 2x^2=8x

0 or 4

Solve each equation by factoring: x^2-4x=0

0 or 4

Evaluate the discriminate for each equation. Determine the number of real solutions.: -4x^2+20x-25=0

1 real solution

Fill in the blank by completing the square: x^2-1/2x+___

1/16

Solve each equation using any method. Round real solutions to the nearest hundredth: 4x^2+4x=3

1/2, -3/2

Simplify: (8- sqrt-1) - (-3+ sqrt-16)

11-5i

Find the value of k that would make the function a perfect square trinomial: x^2+kx+64

16 or -16

Find all solutions to each quadratic equation: 2x^2-4x+7=0

1±1 sqrt10 /2

Solve by completing the square: 5x^2-x-15=0

1±sqrt301 /10

Simplify: (8i)(4i)(-9i)

288i

Solve each equation by finding the square root: 5x^2-40=0

2sqrt2, -2sqrt2

Change from standard form to vertex form: y=3x^2+2x-6

3(x+1/3)^2-19/3

Solve each equation by factoring: 2x^2-x-3

3/2,1

Solve each equation using the Quadratic Formula: x^2=3x-1

3± sqrt5 /2

Solve each equation by finding the square root: 9x^2=25

5/3, -5/3

Simplify: sqrt -50

5i sqrt2

Solve the quadratic equation by completing the square: x^2-12x+7=0

6±sqrt29

Simplify: -5(1+2i) + 3i(3-4i)

7-i

Your bakery sells more bagels when it reduces prices, but then its profit changes. y=-1000x^2+1100x-2.5 models the bakery's daily profit in dollars, where x is the price of bagel in dollars. What's the highest price the bakery can charge, in dollars, and make a profit of at least $200?

86 cents.

Factor each expression: 27p^2-9p+18

9(3p^2-p+2)

Factor each expression: 9x^2-36

9(x+2)(x-2)

Simplify each expression: (-6-5i)(1+3i)

9-23i

In binomials, what is the difference of squares?

A shortcut to factoring when the last term is a perfect square. a^2-b^2=(a+b)(a-b)

How do you find the y of the vertex in standard form?

After you find the x, -b/2a, you have to plug the x in the original equation and solve for y.

How do you find the y of the vertex?

After you find the x, you have to plug the x in the original equation and solve for y.

What does i and i^2 equal?

An imaginary number or sqrt-1. Also, -1

Graph and state the axis of symmetry of y=-3(x+7)^2-8.

Bottom left opening downwards

Plot each complex number and find its absolute value: 2-2i

Bottom right quadrant, 2 sqrt 2

How do you know if something is a perfect square trinomial?

By dividing the b by 2 and then squaring it to see if it matched the value of c.

How can you solve a quadratic function by factoring?

By moving all terms to one side, leaving the other side 0. Then, creating an X-box and solve for the missing variable.

What is GCF in an expression?

GCF is the greatest common factor between all terms in a binomial or trinomial.

Graph and state transformations of f(x)=x^2-1.5

Min at 1.5 and u shaped upwards

Evaluate the discriminate for each equation. Determine the number of real solutions.: x+2=-3x^2

No real solutions

Graph and state the axis of symmetry of f(x)=2(x-2)^2+5.

Small u in the top rightish opening upwards.

What are the ways to solve equations in 4-6?

Solve by square root, solve by perfect square trinomials, and solve by completing the square.

What is the formula for the discriminant and how can you tell how many solutions an equation will have?

The discriminant is b-4ac from the quadratic equation and if the discriminant is positive, there will be 2 solutions, if it's negative, there will be no solutions, and if it's 0, there will be 1 solution.

How can you tell if an equation is a quadratic function?

The x is squared

How is completing the square different from changing forms?

You're doing the same operation on both sides because there should be numbers on both sides. While changing forms, you leave everything on one side.

Solve: x^2-4x+5=0

x= 2±i

Change from standard form to vertex form: y=-x^2+4x-5.

y=-(x-2)^2-1

Write a quadratic function whose graph has a vertex at (3,7) and contains the point (12,0)

y=-7/81(x-3)^2+7

Change from standard form to vertex form: y=2x^2-8x+2.

y=2(x^2-2)^2-6

Change from standard form to vertex form: y=2x^2-8x+2.

y=2(x^2-4)^2-6

What is vertex form, vertex, axis of symmetry equations?

y=a(x-h)^2+k, (h,k), and x=h

What is standard form, x-coordinate of the vertex/axis of symmetry, and y-intercept?

y=ax^2+bx+c, -b/2a, (0,c)