Quadratic Functions (10-1 to 10-3)
Zeroes
Another name for Roots
Find the axis of symmetry y=x^2+2x-15
Axis of Symmetry: x=-1
Find the axis of symmetry y=-x^2-6x-10
Axis of Symmetry: x=-3
Find the axis of symmetry y=0.25x^2+2x+7
Axis of Symmetry: x=-4
Find the axis of symmetry y=-x^2-14x-59
Axis of Symmetry: x=-7
Find the axis of symmetry y=x^2+16x+71
Axis of Symmetry: x=-8
Find the axis of symmetry y=2x^2+36x+170
Axis of Symmetry: x=-9
Find the axis of symmetry y=x^2-2x-5
Axis of Symmetry: x=1
Find the axis of symmetry y=-3x^2 + 12x
Axis of Symmetry: x=2
Find the axis of symmetry y=-2x^2+32x-126
Axis of Symmetry: x=8
Find the axis of symmetry y=-x^2+18x-75
Axis of Symmetry: x=9
Quadratic Function
Described by an equation in the form of f(x)=ax² +bx+c
x=9
Find the axis of symmetry of f(x)=3x²-54x+241
x=-2
Find the axis of symmetry of f(x)=x²+4x+5
x=2
Find the axis of symmetry of y=-3x²+12x-10
x=-8
Find the axis of symmetry of y=x²+16x+64
Define vertex.
Is the maximum or minimum point of the parabola or turning point of the parabola.
Domain
Permissible values for x
Range
Permissible values for y
vertex
The _____ is the lowest point of a parabola that opens up and the highest point of a parabola that opens down
x=-b/2a
The formula for the Axis of Symmetry
Maximum Value
The highest point of a parabola ( when a<0)
Minimum Value
The lowest point of a parabola (when a>0)
Parabola
The name for the shape of the graph of a quadratic function.
Define Axis of Symmetry
The vertical line that divides the parabola into two equal halves.
Roots
The x-intercepts of the parabola
Find the vertex y=x^2+4x
Vertex: (-2,-4)
Find the vertex y=x^2+10x+33
Vertex: (-5,8)
Find the vertex y=x^2+12x+30
Vertex: (-6,-6)
Find the vertex y=x^2-3
Vertex: (0,-3)
Find the vertex y=x^2
Vertex: (0,0)
Find the vertex y=x^2-6x+5
Vertex: (3,-4)
Find the vertex y=5x^2-40x+81
Vertex: (4,1)
Find the vertex y=-3x^2+30x-78
Vertex: (5,-3)
Find the vertex y=x^2-12x+46
Vertex: (6,10)
Find the vertex y=-2x^2+28x-98
Vertex: (7,0)
1 and 3
What are the roots of this function?
x=6
What is the Axis of Symmetry for: f(x)=x²-12x+40
x = 3.5
What is the axis of symmetry of f(x)=x²-7x+9
Axis of symmetry (mathematically)
X = - b/2a
vertex has a x-coordinate of
X = - b/2a, (X,Y)
Exponential Function
a function in which an independent variable appears as an exponent
Linear Function
a function in which the graph of the solutions forms a line
Quadratic Function
a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero
Parabola
a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve
Perfect Square
a square of a whole number
Perfect Square Trinomial
a trinomial in the form a²+2ab+b² or a²+2ab+b²
Zero Of a Function
a value of x that makes the function's value zero
Axis Of Symmetry
A line that divides a figure in half so that each half is the mirror image of the other
Quadratic Equation
ax² + bx + c = 0
Discriminant
b²-4ac
opens down
if the leading coefficient (a) is negative, the parabola
opens up
if the leading coefficient (a) is positive, the parabola
axis of symmetry
the line passing through the vertex that divides the parabola into two symmetric parts called the _____ __ ________
Parent Function
the most basic function of a family of functions, or the original function before a transformation is applied
Vertex
the point of intersection of lines or the point opposite the base of a figure
Roots
the solutions to a quadratic equation
x-intercept
x coordinate of a point where a graph crosses the x axis/ y coordinate of this point is zero
y = 1
y = -x² - 6x - 8 Find y when x = -3
y = -2
y = 2x² -2 . Find y when x = 0
y = 6
y = x² + 6 Find y when x = 0
y = -25
y = x² - 10x Find y when x = 5
y = -10
y = x² - 2x - 9 Find y when x =1
y= -5
y = x² - 6x + 4 Find y when x = 3
y = 0
y = x² Find y when x = 0
y = -3
y= -x² + 10x - 28 Find y when x = 5
y = 4
y= -x² - 4x Find y when x = -2
y= 8
y= x² + 2x + 9 . Find y when x = -1
y=-13
y= x² + 2x - 12 Find y when x=-1
y= -9
y= x² + 8x + 7 . Find y when x = -4
Intercept Form
y=a(x-p)(x-q)
Square Root
√(xy) = √x · √y, a number that when multiplied by itself equals a given number
