GCF
Find the greatest common factor of 12 and 18.
6
Given the parabola with equation y = (x-2)^2 + 3, state the domain and range.
Domain: all real numbers. Range: y > 3.
Use the box method to multiply: (x+2)(x+3).
SHOW YOUR WORK!
x^2 + 5x + 6
Describe the end behavior (as x \to \pm\infty) of y = x^2.
As x \to \infty, y \to \infty; as x \to -\infty, y \to \infty (parabola opens up).
Find the GCF of the terms 6x^2 and 15x.
GCF of 6x^2 and 15x is 3x.
The graph of a parabola opens downward with vertex at (1,4). State the domain and range.
Domain: all real numbers. Range: y < 4 (since opens downward).
Multiply using the box method: (2x+1)(x-4).
SHOW YOUR WORK!
2x^2 -7x -4.
Describe the end behavior of y = -3x^2 + 2x -1.
As x \to \infty, y \to -\infty; as x \to -\infty, y \to -\infty (opens down because leading coefficient is negative).
Factor out the greatest common factor from 8x^3 + 12x^2.
8x^3 + 12x^2 = 4x^2(2x + 3)
For the parabola given by y = -2(x+3)^2 + 5, determine the domain and range and explain how the coefficient affects the range.
Domain: all real numbers. Range: y < 5
Multiply using the box method and simplify: (3x-2)(2x+5).
SHOW YOUR WORK!
6x^2 +11x -10.
Explain how the coefficient a in y = ax^2 + bx + c determines the end behavior of the parabola for large positive and negative x.
DOUBLE JEOPARDY!
- name 4 professions that involve the application of math
Determine the GCF and factor it out from the trinomial 14x^3 - 21x^2 + 7x.
7x(2x^2 -3x +1)
A parabola has vertex (0,-2) and passes through (2,6). State the domain and range.
Domain: all real numbers, Range: y > -2
Use the box method to expand: (x^2+2x)(x+3) and write the result in standard polynomial form.
SHOW YOUR WORK!
x^3 +5x^2 +6x.
Compare end behavior of y = 0.5x^2 and y = -0.5x^2 and explain what happens to the outputs as x \to \infty.
For y = 0.5x^2, as x \to \infty, y \to \infty and as x \to -\infty, y \to \infty. For y = -0.5x^2, both ends go to -\infty.
For the polynomial 18x^4y^2 - 24x^3y^3 + 30x^2y, find the greatest common factor
6x^2y
State the domain, range, vertex, increasing interval and decreasing interval, and sign of the quadratic function drawn on the board.
Multiply using the box method and combine like terms: (x+4)(x^2-3x+2).
SHOW YOUR WORK!
x^3 +x^2 -10x +8.
Given two quadratic functions, f(x)=2x^2+3x-1 and g(x)=-2x^2 + x + 5, describe and contrast their end behaviors and explain how those behaviors relate to the leading coefficients.
f(x)=2x^2+3x-1 (leading 2>0) both ends \to \infty
g(x)=-2x^2+x+5 (leading -2<0) both ends \to -\infty.