WEST-E Tier 2

What are the coordinates of the y-intercept of the equation 5x - 3y = 2?

(0, -2/3) Explanation: Let x = 0 and solve for y. The video provides examples illustrating how to find the x and y intercepts.

Find the y-intercept of this line: 3x - 9y = -27

(0, 3)

Find the x-intercept of this line: 12x - 6y = 24

(2, 0)

What are the coordinates of the x-intercept of the equation 2x - 3y = 8?

(4, 0) Explanation Let y = 0 and solve for x:

Binomial Theorem

(a+b)^n = ∑(n choose k)a^(n-k) * b^k

What is the x value of the high or low point of the parabola f(x) = x^2 + 1?

0 h = -b/(2a) where h is the x value

A quadrilateral function graph shows the function crossing the x axis at two spots, how many solutions are there? How many are imaginary?

2 0 The solutions are real, because the graph crosses the x-axis at two points.

What number is left inside the radical after you simplify? cuberoot(192)

3 Explanation cubed root of 192 = cubed root of 64 * cubed root of 3 = 4 * cubed root of 3

Simplify. (3/x)/((y/x)+3)

3/(3x+y)

The factored form of a polynomial function is f(x) = (x + 4)(x - 2)(x - 1)(x + 1). According to the Fundamental Theorem of Algebra, what is the degree of this function?

4

Simplify: √175

5sqrt7

What is the slope of the line represented by the following formula? y = 2 + 6(x - 3)

6

Fundamental Theorem of Algebra

A polynomial will have as many roots as its degree

What are the three ways to prove two triangles are similar?

AA, SAS, SSS

Find the derivative F(x)=e^2x

Chain rule Y'= 2e^2x

What is the difference between equal and equivalent sets?

Equal - same elements in set Equivalent - same number of elements in set

What three transformations to the parent function are represented in this polynomial: f(x) = -(x + 2)^3 + 3 ?

Flip, move left, and move up

Which of the following equations represent(s) a line that goes through the points (2,3) and (1,1)? I) y = 2(x - 2) + 3 II) y = 2x - 1 III) y = 2(x - 1) + 1

I, II, & III

In this rational function, what is the location of a horizontal asymptote? (4x +3 )/ (2x-8)

If the numerator and denominator have the same largest exponent, the ratio of the numerator and denominator will define a horizontal asymptote. In this case, y = 4/2 = 2.

Solve. 4x + 2x + 6 = 6x + 2 + 4

Infinite Solutions

y = (x+2)^2 What transformation is occurring in this function?

Left two units

Solve. 3x + 4 + 4x + 8 = 2x + 5x + 10

No solutions

Solve |x| = -3

Not possible

Parameter vs. Statistic

Parameter: a characteristic or measure of a POPULATION Statistic: a characteristic or measure of SAMPLE

Two solutions of the function f(x) = x^3 + 5x^2 - 9x - 45 are x = 3 and x = -3. How many solutions and what types of solutions remain?

The polynomial function has a degree of 3, so only one solution remains. Imaginary solutions occur in conjugate pairs for polynomial functions with real coefficients, so the remaining solution must be a real number.

Find the derivative of y=2x

Y prime= 2

Expand (a + b)^3

a^3 + 3a^2b + 3ab^2 + b^3

A polynomial graph will have at most ____________ turns

one less than its degree amount of

Odd degree function starts and ends on...

opposite sides of the x axis

sqrt(x) * sqrt(y) = ?

sqrt (xy)

Even degree function starts and ends on ...

the same side of the x axis

Solve |x + 1| < 2

x < 1 AND x > -3

Solve for x 3/(x+2) + 7/ (x+1) = 3/(x^2 +3x + 2)

x = (-14)/(10)

Solve the equation below. 0 = x^2 + 7x +12

x= -3, -4

Binomial Theorem - (x ± a)^3

x^(3) ± 3ax^(2) + 3a^(2)*x ± a^(3)