VOCAB
This is the standard form of a quadratic equation.
True or False :
y = x2 + 8x + 15 factored is (x + 4)(x + 2) ?
False: (x + 3)(x + 5)
y = a(x - p)(x - q)
Factored or Intercept Form
The vertex of: y = (x+1)2 + 2
What is (-1,2) ?
Standard Form: x2 + 6x + 50
What is the y-intercept?
What is 50?
Convert to vertex form: f(x) = x2 + 4x - 1
f(x) = (x + 2)2 - 5
What is the formula for the discriminant?
b2 - 4ac
The lowest or highest point on a parabola.
What is the VERTEX?
(Maximum or Minimum respectively...)
True or False: x2 - 11x + 24
Factored is: (x - 3)(x - 8)
True, it multiplies and works.
Solve for the factors / solutions / zeroes?
(x - 4)(x + 6)
4 and -6
The vertex of: y = (x+3)2
What is (-3, 0)
The leading coefficient being negative means
There is a reflection across the x-axis, concave DOWN
Convert to vertex form f(x) = -2x2 + 8x - 8
f(x) = -2(x - 2)2
y = 3x2 - 2x - 4
Find the discriminant b2 - 4ac and how many zeroes?
52, two real
The line that passes through the vertex and divides a parabola into two symmetric parts.
What is the AXIS OF SYMMETRY?
True or False: x2 + 5x - 24
Factored is: (x + 3)(x + 8)
False: Watch the signs:
Factored is: (x - 3)(x + 8)
Solve for the factors / solutions / zeroes?
(3x - 4)(x - 1)
4/3 and 1
Give the formula for vertex form
What is f(x) = a(x-h)2 + k
The axis of symmetry: y= -x2 + 2x + 1
What is x = 1
Convert to vertex form: f(x) = -2x2 + 4x - 9
f(x) = -2(x - 1)2 - 7
y = 4x2 + x + 6
Find the discriminant b2 - 4ac and how many zeroes?
-95, No real or two non real
The u-shaped graph shown by a quadratic.
What is a PARABOLA?
Name the term that defines all of the possible x-values of a function
What is Domain
Solve for the factors / solutions / zeroes?
x(x + 7)
0 and -7
The transformations the graph: y = - 2 ( x+4 )2 - 1
What is reflected over x-axis, vertical stretch of 2, shifts left 4 units and shifts down 1 unit?
Give the general form of standard form
What is f(x) = ax2 + bx + c
State the transformations on f(x) = 8x2 -16x + 27
Vertical stretch of 8, shifted right 1, and shifted up 19
y = x2 - 8x + 16
Find the discriminant b2 - 4ac and how many zeroes?
0, one real solution, the VERTEX
These are four names for the place or places a parabola crosses the x-axis.
What are x-intercepts, roots, solutions and zeros?
Name the polynomial whose middle term, divided by two and then squared, is equivalent to the product of 'a' and 'c'.
Example: x2 - 6x + 9 = (x - 3)(x - 3)
What is a Perfect Square Trinomial?
Solve for the factors / solutions / zeroes?
(3x + 5)(7x - 2)
-5/3 and 2/7
Write the equation for a parabola that makes the following translations: opens downward, shifts right 5 units and shifts upwards 8 units.
What is y = - (x-5 )2 + 8 ?
F ind the vertex of: y = x2 - 12x + 4
(Completing the square)
Rewritten: (x - 6)2 - 32
What is (6, -32)?
State the transformations on -5x2 - 37 + f(x) = -10x
vertical stretch of 5, shifted right 1, shifted up 32
y = x2 + 7x + 10
Find the discriminant b2 - 4ac and how many zeroes?
9, two real and rational solutions