Alg Sem 2 Review

Definitions

100

What is an x-intercept? 

When y = 0, zeros, when a graph crosses the x -axis 

200

What makes a function a quadratic equation? 

The x²

300

What is a maximum or minimum value?

The y-coordinate of a vertex

400

What is the zero product property? 

When factors are set = to zero to solve for the x-intercepts

500

What is the simplest radical form? 

When a radical is simplified as much as possible

i.e. Sqrt (125) = 5sqrt5

Methods of Solving

100

What is the Quadratic Formula? 

x = (-b +- sqrt(b² - 4ac))/2a

200

When completing the square, what are the four steps? 

1) Multiple by the leading coefficient

2) Add b²/4a to both sides 

3) Square root 1st and 3rd 

4) Solve using the square root property 

300

Rewrite the quadratic function in intercept form: 

f(x) = 3x² - 3x - 90 

f(x) = 3(x + 5)(x - 6) 

400

Determine the vertex and x-intercepts from this quadratic function using any method.

h(x) = 3x² - 6x - 72 

x -intercepts: 4 and -6 

Vertex (1, -75) 

500

Rewrite the quadratic function from standard form to vertex form: 

g(x) = 4x² +32x -16 

 g(x) = 4(x + 4)² - 48 

Graphs

100

Graph the line y = -2x + 3 

b = 3 and m = -2 

200

Solve the System of Equations by Graphing 

y = -1/2x + 3 

x + 2y = 6 

Infinitely Many Solutions 

300

Graph the Function and determine the zeros

y = 4x² + 2x -6 

Zeros = -1.5 and 1 

400

Solve the System of Inequalities by Graphing: 

y > 2/3x - 1 

y < -4x + 1 

See Desmos 

500

Write the System of Inequalities for this graph 

Answer 

Polynomials

100

What are 3/4 reasons that an expressing is a nonmonomial? 

Negative Exponent

Multiple Terms

Variable in the Denominator

Variable in the Exponent 

200

Find the product: (12x³yz³⁾(-2xy)(3yz⁴)

-72x⁴y³z⁷

300

What is the degree, leading Coefficient and classification of this Polynomial: 45x² + 12x - 3x³ 

Degree = 3 

Leading Coefficient = - 3 

Classification = Trinomial 

400

Find the Product: (3x - 12)(-2x + 4) 

-6x² + 36x - 48 

500

Find the product: (12x -3)²(-4x + 1) 

-576x³ + 432x² - 108x + 9 

Factoring and Square Roots

100

Factor the quadratic expression: x² - 13x - 48 

(x + 3)(x - 16) 

200

Factor the Quadratic: 2x² -6x - 20 = 0 

(2x + 4)(x - 5) 

300

Factor the Quadratic: 25x⁴ + 15x³ + 5x²

5x²(5x² + 3x + 1) 

400

Use the Square Root Property to Solve 

-12(x² + 3) -10 = -58 

x = -1 and 1 

500

Solve the Quadratic by Factoring: 

6x² - 23x + 20 

(2x - 5)(3x - 4)