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)
