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binomial

A polynomial with two terms

coordinate

The number that corresponds to a point on a number line

coefficent

the number in front of the variable

orgin

the coordinate (0,0)

inequality

A mathematical sentence that shows the relationship between quantities that are not equivalent

expression

A mathematical phrase without an equal sign.

Evaluate

To find the value of a mathematical expression.

quadratic

2nd degree

Equation

A mathematical sentence that contains an equals sign

reciprocal

One of two numbers whose product is 1; it is also called multiplicative inverse.

solve

The process used to find the value or values that make an equation true.

vertex

The point where two sides meet. (Shared end points of the line segments of a polygon.)

Axis of Symmetry

a line that divides a parabola in two equal halves and goes through the vertex

roots

the solutions to a quadratic equation

linear

A relationship that graphs as a straight line. This means y is changing at a constant enterval.

Quadratic standard form

y = ax² + bx + c

GCF

Greatest Common Factor

D.O.T.S.

Difference of 2 squares

M/C Chart

factoring the trinomial by using the multiplacation number and the combine number

Factor Completely

factoring by using at least 2 different methods

leading coefficient

The coefficient of the term with the highest degree

Coefficient

the decimal part

quadratic equation

ax² + bx + c = 0

Symmetry

A plane figure that can be folded along a line so the two parts match.

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

Parent Function

the most basic function of a family of functions, or the original function before a transformation is applied

Minimum Value

The lowest point of a parabola (when a>0)

Maximum Value

The highest point of a parabola ( when a<0)

y=a(x-p)(x-q)

Intercept Form

x-intercept

the point where the line crosses the x-axis

Square Root

when multiplying a number by itself to get a square number

Zero Of a Function

a value of x that makes the function's value zero

Perfect Square

the number that forms when two same numbers are multiplied together

Linear Function

y = mx + b

Exponential Function

y = ab^x

discriminant

b²-4ac

Axis of symmetry (mathematically)

X = - b/2a

Parabola

the graph of a quadratic function

domain of parabola

all real numbers

translate or shift

move up or down

wide parabola

small coefficient of X

narrow parabola

large coefficient of X

Minimum

the lowest possible y value for the graph of a quadratic function; also the y -coordinate of the vertex

Maximum

the highest possible y value for the graph of a quadratic function; also the y-coordinate of the vertex

AOS

The axis of symmetry. Also, the line that goes through the center of a parabola.

standard form

y = ax^2 + bx + c

Domain

The ______________________ is all the possible INPUT, X, values.

Range

The difference between the greatest number and the least number in a set of data.

vertex form

y = a(x - h)^2 + k

intercept form

y= a(x - p)(x - q)

terms

A number, a variable, or the product of a number and a variable

trinomial

A polynomial with 3 terms

y-intercept

the point where the line crosses the y-axis

X-intercepts

the point on a graph where y = 0, also points where the graph crosses the x-axis

methods for solving

factoring, square root method, completing the square, quadratic formula and graphing

i

imaginary number, the square root of -1

-1

i squared

complex number

includes real and imaginary numbers

x=-1

f(x) = -2(x-3)(x+5). Axis of symmetry is

x=2.5

f(x) = x²-5x+3. Axis of symmetry is

f(x)≤-5

f(x) = -3(x+4)²-5. Range is

f(x) ≥-1

f(x) = x²+2x. Range is

(0, 9)

f(x)= -¾(x+4)(x-3). y-intercept is

(0, -2.5)

f(x)=½(x-1)²-3. y-intercept is

-2, -6, -10, -14, ...

f(x)=-2x²-4x+9. First differences from vertex are....

1/4, 3/4, 5/4, 7/4, ...

f(x)=¼(x+7)²-2. First differences from vertex are...

f(x)=5(x-7)(x+2). x-intercepts are

(7, 0) and (-2, 0)

(8, 0) and (2, 0)

f(x) = (x-5)²-9. x-intercepts are

(11, 12)

Axis of symmetry is x=5 and point (-1, 12) is on the graph. Another point is

(-11, 0)

Vertex is (-4, 13) and x-intercept is (3, 0). The other x-intercept is

FOIL, distribute and combine like terms

To convert Vertex Form to Standard Form you must

To convert Factored Form to Vertex Form you must

Average the x-intercepts and plug that number in to find the vertex. Keep the leading coefficient.

FOIL

To convert Factored Form to Standard Form you must

To convert Standard Form to Vertex Form you must

Find -b/2a and plug that number in to find the vertex. Keep the leading coefficient.

To find the x-intercepts with Standard Form you must

Re-write into Factored Form by factoring, or use the Quadratic Formula

To find the leading coefficient if you know the x-intercepts and another point.

Write a Factored Form equation with the x-intercepts and solve for 'a' with the other point.

Write in Vertex Form and solve for 'a' with the other point.

To find the leading coefficient if you know the vertex and another point.

The second differences are constant and equal to 2a (twice leading coefficient)

What is always true about the 2nd differences for a quadratic equation?

Maximum because a≤0

f(x)=3+2x-x² has a minimim or maximum point?

f(x)=-(x-2)(x+6)

How do you factor f(x)=-x²-4x+12?

f(x)=-x(3x-5)

How do you factor f(x)=-3x²+5x?

<0 (no answers), =0 (1 answer), >0 (2 answers)

What does the value of the discriminant tell you?

f(x)= (3x-4)(3x+4)

How do you factor f(x) = 9x²-16?

f(x)= (5x-1)(x+3)

How do you factor f(x) = 5x²+14x-3?

Leading coefficient = -3. How do you plot points starting at the vertex?

Over 1 each way and down 3, then over 1 each way and down 9, then over 1 each way and down 15, etc.

Minus 2 from both sides. Square both sides. Minus 3 from both sides.

How do you find the quadratic equation that has solutions of x = 2 ±√3?

How do you solve 3x²=4x-11?

Make one side = 0. Try to factor, or find a, b, c and use the Quadratic Formula

(4±√7)/3

How do you simplify (8±√28)/6?

x ≈ 1 and x ≈ -9.

The x-intercepts are x=-4±√23. When you plot them on the x-axis they are close to which integer values?