Algebra 2/Trig Midterm review

Solve and graph equations and inequalities Radical equations:

Solve and graph equations and inequalities Radical equations:

Absolute value Solve and check:

Absolute value Solve and check:

Quadratic equations Solve:

Quadratic equations Solve:

#2 Set = o: -43

# 3 Factor:

quadratics Complete the square to solve: 3x 2 +6x-45=0 When will a ball hit the ground, where will it be after 5 seconds what will it’s max height be? h(t) = -2t 2 +40t+4 t is in seconds

Answers: Divide out the 3: 3x 2 +6x-45=0 X 2 +2x -15 =0 X 2 + 2x + 1 = (x + 1) 2 = 16 X+ 1 = 4 and x + 1 = -4 X = 3 x =-5

Graph: When will a ball hit the ground, where will it be after 5 seconds what will is max height be,given h(t) = -2t 2 +40t When t = 20, it hits the ground. After 5 seconds it is 154 ft.high and it reaches a max height of 204 ft.

Rational expressions and equations Simplify:

Rational expressions Simplify:

Solution: Second one:

Complex Fractions Simplify:

Complex Fractions Simplify:

adding Find the lcd and add:

adding lcd = (x+1)(x-1)

Rational equations Multiply by lcd and solve:

Rational equations Lcd = a(a-3) 3 is extraneous

grouping Factor and simplify:

grouping Factor and simplify:

Functions Domain- left to right – x values Range – bottom to top – y values Restricted domains: Set denominators = to 0 Set radicands f -1 (x) inverse: swap x & y and solve Varies inversely: xy = xy

Domain and range: Find the largest range for: Y = 3x – 7 For the domain:

Domain and range: Find the largest range for: Y = 3x – 7 For the domain: When x = 3, y = 3(3) – 7 =2 Which is the largest value for that domain

Examples: Find the domain:

Examples: Find the domain: Because it is a denominator and a radical

Examples: Find the domain: above x axis: -35

Compositions: Second function inside first: Let f(x) = x g(x) = x - 3

Compositions: Second function inside first: Let f(x) = x g(x) = x - 3

Inverses:

Multiply each side by the reciprocal

Irrationals Simplify:

Irrationals Simplify:

rationalizing Rationalize using conjugates:

rationalizing Rationalize using conjugates:

Complex numbers: Remember:

Examples: Evaluate:

Examples: Evaluate:

The discriminant If b 2 – 4ac is…. < 0 (negative) roots are IMAGINARY = 0 roots are rational and equal > 0, perfect square, roots: rational & unequal > 0, not perf. Sq., roots: irrational & unequal Ex: The roots of ax x = -9 are rational and equal when a = ?

Answer: ax x = -9 ax x + 9 =0 Set b 2 – 4ac = – 4(a)(9)= a=0 36a=144 a=4

Formulas: Quadratics: x= Sum = -b/a Product = c/a

Conjugate roots: If 3 – 2i is a root, so is 3 + 2i Find the equation that has the root 4 – i STEPS: 1. Find the sum & the product of 4 – i and its conjugate 2. use x 2 – sum(x) + product = 0

SOLUTION: SUM =PRODUCT =

circles Write the equation of a circle with center at (-2,3) and a point on the circle (1,1) Graph the circle, find the radius using pythagorean theorem and use equation above.

answer Radius = Center = (-2,3)

Complete the square for circles Example:

Complete the square for circles Example:

Solving exponential equations Find like bases and set the exponents equal:

Solving exponential equations Find like bases and set the exponents equal: