Quadratic Functions (10-1 to 10-3)

Ace your homework & exams now with Quizwiz!

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


Related study sets

ch. 1 - mental health and mental illness

View Set

Audit Ch 15, CH 15 (TB), AC 432 Chp 15, chapter 17, Audit Ch 15, Audit Ch 15, Chapter 15, Audit Ch 15, Audit Ch 15, Chapter 15 Exam 2, Audit Ch 15, Audit Ch. 8 MC, Auditing Profession and Planning

View Set

Macroeconomics ch. 12 (pt 1&2 not on ashtyns and 3-5)

View Set

D076 - Finance by ME (Lesson Checks)

View Set

The Practice of Mental Health/Psychiatric Nursing

View Set

Apply It: Chapter 5 Short Workplace Messages and Digital Media

View Set

Exam #2 Knowledge Check Questions

View Set

Biochemistry Exam 2: Chapter 9 (Nucleic Acids: How Structure Conveys Information)

View Set