Algebra II Unit 3

4y is the greatest common factor of 4y^2 + 6y.

False

A quadratic equation factored to 0 = (x-4)(x+3) would have solutions of x = -4 and x = 3.

False

The vertex of a parabola will never be on the axis of symmetry.

False

The vertex of f(x) = 2(x-2)^2 +10 is (-2, 10).

False

When solving a quadratic equation by completing the square, the coefficient of the highest power must be any positive integer.

False

4n^3 + 5n^2 + 6n + 15 factors to (3n^2 + 2) (3n + 5).

False; This factors to (2n2 + 3)(2n + 5).

Write y = -3x^2 + 12x - 21 in vertex form.

y = -3(x - 2)^2 - 9

Write y = -4x^2 - 64x - 265 in vertex form.

y = -4(x + 8)^2 - 9

Find the quadratic function y=ax^2+c with a graph that includes (0, 1/2) and (-3, 73/2)

y=4x^2+1/2

Factor 4x^2 + 5x - 21

(4x - 7)(x + 3)

Factor 4y^2 - 3y - 1

(4y + 1)(y - 1)

Factor 18ab + 9ax -4b - 2x.

(9a - 2)(2b + x)

Solve -4x^2 - 16x - 7 = 0 by graphing. If necessary, round your answer to the nearest tenth.

-3.5, -0.5

Simplify (3 + 3i) - (7 + 6i).

-4 - 3i

Factor f^2 - 12f + 36.

(f - 6)^2

Factor m^3 - 4m^2 + 6m - 24.

(m - 4)(m^2 + 6)

Factor pq + 4q - 2p - 8.

(p + 4)(q - 2)

Factor t^2 - 10t + 25.

(t - 5)^2

Factor xy - 6 + 2y - 3x.

(x + 2)(y - 3)

Factor x^2 + 5x + 6.

(x + 3)(x + 2)

An expression for the area of a rectangle is xy - 2x + 3y - 6. Express this area in factored form.

(x + 3)(y - 2)

Factor x^2 - 16.

(x + 4)(x - 4)

Factor x^2 + 3x - 10.

(x + 5)(x - 2)

Factor x^2 - 15x + 54.

(x - 9)(x - 6)

Factor 3x^3 + 2x^2y + 3xy^2 + 2y^3.

(x^2 + y^2)(3x + 2y)

Identify the vertex and y-intercept of the graph of f(x) = -4(x + 3)^2 + 7.

(-3, 7), y-intercept -29

Identify the vertex and y-intercept of the graph of f(x) = -3(x + 6)^2 + 9.

(-6, 9), y-intercept -99

Factor 4x^2 - 49.

(2x + 7)(2x - 7)

Complete the square: x^2 + 2x + ____ .

1

Write 1-√16 in the form a+bi

1 - 4i

Without graphing, tell how many x-intercepts y= 2x^2 + 4x + 2 has.

1 intercept

Simplify √-500 using the imaginary number i.

10i√5

Find the GCF of 14a^2b^4c and 56ab^2c^2

14ab^2c

Find the GCF of 54a^2, 84ab, and 10c.

2

Use the GCF to factor 15x^2 + 6x.

3x(5x + 2)

A rocket is launched from atop a 63-foot cliff with an initial velocity of 95 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t^2 + 95t + 63. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest hundredth of a second.

6.54 sec

The graph of y = -2x^2 + 15x + c contains (3, 89). Find the value of c.

62

A rocket is launched from atop a 54-foot cliff with an initial velocity of 119 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t^2 + 119t + 54. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest hundredth of a second.

7.87 sec

A biologist took a count of the number of migrating geese in a state park and recounted the park's population of geese for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of geese at the lake on week 8.

P(x)= 42x2 - 186x + 762; 1962 geese

A biologist took a count of the number of migrating geese in a state park and recounted the park's population of geese for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of geese at the lake on week 8.

P(x)= 42x^2 - 186x + 762; 1962 geese

3x^2 -5x - 2 factors to (3x+1)(x-2).

True

The minimum value of a parabola that opens upward will be its vertex.

True

The square root of a negative number is an imaginary number.

True

The vertex of f(x) = 3(x+2)^2 - 4 is (-2,-4).

True

Using the quadratic formula allows you to find the x-intercepts of a quadratic equation.

True

Randex Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = -2x^2 + 4x + 2 where x is the number of units produced per week, in thousands. a. How many units should the company produce per week to earn the maximum profit? b. Find the maximum weekly profit.

a. 1000 units; b. $400

Lane Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = -4x^2 + 24x + 3 where x is the number of units produced per week, in thousands. a. How many units should the company produce per week to earn the maximum profit? b. Find the maximum weekly profit.

a. 3000 units; b. $3900

Factor 8a^4b - 3ab^2c.

ab(8a^3 - 3bc)

Find a quadratic model for the values in the table. x | -5 | -4 | -3 | -2 ------------------------- f(x) | 217 | 135 | 73 | 31

f(x) = 10x^2 + 8x + 7

Graph y=1/2x^2+3x+4. Find the minimum or maximum value.

min at y=-1/2

What kind of solutions does ax^2 - bx + c = 0 have if b^2 - 4ac < 0?

two complex solutions

Evaluate the discriminant of 25x^2 + 350x + 49 = 0. Tell how many solutions the equation has and whether the solutions are real or imaginary.

two real solutions

Graph y=-1/3x^2-2x-4. Label the vertex and axis of symmetry

vertex: (-3, -1); x=-3

Identify the vertex and the axis of symmetry of the parabola.

vertex: (1, -6); axis of symmetry: x = 1

Identify the vertex and the axis of symmetry of the parabola.

vetex: (3/2, 25/4); axis of symmetry: x=3/2

Solve x^2 - 4x - 5 = 0 by factoring.

x = -1, x = 5

Solve x^2 - 6x = 0 by graphing or by factoring.

x = 0, x = 6

Solve 6x^2 = 48. If necessary, round your answer to the nearest hundredth.

x=+/-2 √2 ≈ +/-2.83

Solve 7x^2 + 28x = 49 by completing the square.

x=-2 +/-√11

Solve x^2 + 6x - 2 = 0 by completing the square.

x=-3 +/-√11

Solve 9x^2 + 6x + 1 = 64.

x=-3, x=7/3

Solve -11x + 9 + 5x^2 = 0 using the Quadratic Formula.

x=11+/-i √59 / 10

Solve x^2 - 5x - 1 = 0 using the Quadratic Formula. Find the exact solutions. Then approximate any radical solutions. Round to the nearest hundredth.

x=5+/- √29 / 2; -0.19, 5.19

Solve -9x + 6 + 5x^2 = 0 using the Quadratic Formula.

x=9+/-i √39 / 10

Rewrite y = x^2 + 4x + 5 in vertex form. Then find the vertex.

y = (x + 2)^2 + 1; (-2, 1)

Write the equation of the parabola with vertex (-3, -4) and point (-5, 0) in vertex form.

y = (x + 3^2 - 4

Write the equation of the parabola in vertex form.

y = - (x - 3)2 + 2