Wateen's Group
What is the formula for the difference of squares?
a^2 - b^2 = (a + b)(a - b)
What is a perfect square trinomial? Give an example.
It’s a trinomial that factors into a binomial squared; e.g. x^2 + 6x + 9 = (x + 3)^2
What is the general form of a quadratic function?
y = ax^2 + bx + c
Factor: x^2 + 2x + 1
(x + 1)^2
What is the shape of a quadratic graph?
A parabola
Factor: x^2 - 49
(x + 7)(x - 7)
Factor: x^2 + 6x + 9
(x + 3)^2
Identify the vertex of y = (x - 2)^2 + 3
Vertex: (2, 3)
Factor: x^2 - 16
(x + 4)(x - 4)
What does the sign of the coefficient of x^2 tell you?
If positive, parabola opens upward; if negative, opens downward
4x^2 - 81
(2x + 9)(2x - 9)
Is x^2 + 10x + 25 a perfect square trinomial? Explain.
Yes; it’s (x + 5)^2, since \sqrt{25} = 5 and 2 \cdot 5 = 10
Find the axis of symmetry: y = -x^2 + 4x - 1
x = -\b/2a = 2
Factor: 25x^2 - 40x + 16
(5x - 4)^2
Find the y-intercept: y = x^2 - 5x + 6
y-intercept: 6
x^2 - 25 = 0
x^2 - 25 = 0
Expand: (2x - 3)^2
Expand: (2x - 3)^2
Identify vertex, axis, and direction for y = x^2 - 4x + 3
Vertex: (2, -1), Axis: x = 2, Opens upward
Solve: 4x^2 - 9 = 0
x = postive negative 3/2
Find the vertex: y = -2x^2 + 8x - 5
Vertex: (2, 3)
9x^2y^2 - 16z^2
(3xy + 4z)(3xy - 4z)
Solve: x^2 + 12x + 36 = 0 by factoring
(x + 6)^2 = 0 \--> x = -6
Compare y = x^2 and y = (x - 1)^2 - 2
Shifted right 1 and down 2 from y = x^2
Factor: 81x^4 - 16
(9x^2 + 4)(9x^2 - 4) = (9x^2 + 4)(3x + 2)(3x - 2)
Convert to vertex form: y = x^2 + 6x + 5
y = (x + 3)^2 - 4