Test Answers on algebra

Quadratic function A function that can be written in the form f(x) = ax^2+bx+c, where a,b,and c are real numbers and a ≠ 0 Parabola the graph of a quadratic function Vertex form of a quadratic function y = a(x-h)^2 + k Intercept form of a quadratic function y = a(x-p)(x-q) Maximum Value the y-coordinate […]

What is an equation for a direct variation whose graph passes through the point (-5, 3)? y=-3/5x Which line, having the given slope and passing through the given point, represents a direct variation? m= 2/3 ; (9, 6) The length of an object’s shadow varies directly with its height. If a can that is 13 […]

What are the domain and range of mc016-1.jpg? domain: x > 0; range: all real numbers Which is the graph of a logarithmic function? a                                                              […]

ALIBATA 3 patinig (a, e/i, o/u); 14 katinig =17 Alpabetong Romano/ Abecedario Ang pinalit ng kastila ABAKADA Lope K. Santos; 5 patinig +15 katinig= 20 letra Lope K. Santos Ama ng Barirala 1976 Dagdag na 11 letra 1987 (Alpabetong Filipino) 5 patinig + 23 katinig = 28 letra >kautusan pangkagawaran >Blg. 81 2001 Revisyon ng […]

(1a1) Types of numbers: Natural, Whole, Integers, Rational, Irrational, real (1a2) Add Fractions 1) Convert to common denominator 2) Add the numerators 3) Reduce the fraction (1a3) Find opposite of a fraction 1) Switch numerator and denominator 2) Change sign (1a4) Subtract two negative numbers -1 -2 = -3 (1a5) Subtract 1 – (-2) 1 […]

find a number that is 56 less than its square -7, 8 find two consecutive odd integers the sum of whose squares is 130 -9,-7 ,9 or 7 two ships leave port, one sailing east and the other south, some time later they are leaving 17 mi apart, with the eastbound ship 7 mi farther […]

Factoring The process of writing a number or exponent as a product. Factorization Any combination of factors multiplied together resulting in the product Factors Any set of the numbers or expressions that form a product Prime factorization The unique factorization of a natural number written as a product of primes Greatest common factor GCF Product […]

Algebra one of the main branches of mathematics, it concerns the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers, variables, and polynomials, along with their factorization and determining their roots. In addition to working directly with numbers, algebra also covers symbols, variables, and set elements. Addition and multiplication […]

slope intercept form y=mx=b slope formula change in y over change in x regression STAT, EDIT, L1, L2, STAT, CALC, LinReg (ax+b), calculate, E a=slope b=Y-intercept composite functions plug the x value into the equation and solve composite functions: substitution plug the other function in for x transformations y=a(x-h)^2+k a=if negative, refection over the x-axis […]

the identity function f(x)=x the squaring function f(x)=x² The cubing function f(x)=x³ the reciprocal function f(x)=(1/x) the square root function f(x)=√x the exponential function f(x)=eⁿ the natural logarithm function f(x)=ln x the greatest integer function f(x)=int (x) the absolute value function f(x)=abs(x) the sine function f(x)=sin x the basic logistc function f(x)=(1)/(1+e⁻ⁿ) the cosine function […]

natural numbers counting numbers N natural numbers symbol W whole numbers symbol whole numbers starting at zero and counting up intergers postive and negative whole numbers Z intergers symbol rational numbers 2/3, 3.81 Q rational numbers symbol irrational numbers pi real numbers the rational and irrational fancy R real numbers symbol imaginary numbers square root […]

Abscissa The first coordinate in an ordered pair. For the point (8, -2) the abscissa is 8. Absolute Value Absolute value makes a negative number positive. Positive numbers and 0 are left unchanged. The absolute value of x is written |x|. We write |-6| = 6 and |8| = 8. Absolute Value Rules Algebra rules […]

scientific notation a * 10^n; 1 <= a < 10, n an integer, a in decimal form nth Root For a natural number n and a and b real numbers: a is an nth root of b if a^n = b Number of Real nth Roots of b, if b > 0 and n is […]

Producing Equivalent Equations by adding the same quantity to both sides of an equation If we start with the equation a=b, then adding \”c\” to both sides of the equation, we get a + c = b + c. Producing Equivalent Equations by subtracting the same quantity from both sides of an equation If we […]

f(x)=ax^2+bx+c is a parabola with a turning point called a vertex. axis of symmetry equation is quadratic equation An equation that can be written in the form ax2 + bx + c = 0, where a,b,and c are real numbers and a ≠ 0 zero product property If the product of two factors is zero, […]

Matrix Outcomes Unique Solution, No Solution, Infinite Solutions Unique Solution Indicates the system is consistent. No Solution Indicates the system is inconsistent. In Gauss Jordan Elimination, if a zero appears on the left side and a non zero appear on the right side of the row, the system has no solution. Infinite Solutions Indicate the […]

To find X-intercepts Solve f(x)=0, (ordered pair) To find y-intercepts Find y= f(0), (ordered pair) Even Functions Symmetric about the y-axis, f(-x)=f(x) Odd Functions Symmetric about the origin, f(-x)=-f(x) f(x)+k Vertical Shift Up f(x)-k Vertical Shift Down f(x+h) Horizontal shift left f(x-h) horizontal shift right -f(x) Vertical reflection over X-axis (x,-y) f(-x) Horizontal reflection over […]

Distance formula √(x2-x1)²+(y2-y1)² Quadratic formula (-b±√b²-4ac)/2a Standard form ax²+bx+c How do you rationalize the denominator with a radical? lol How do you find x intercepts? set y or f(x) = 0 How do you find y intercepts? set x=0 slope formula y=mx+b point slope formula (y-y1)=m(x-x1) average rate of change or AROT f(x)-f(c) all over […]

Series ai=a1+a2+a3+……an The Sum of a Finite Arithmetic Sequence Sn=n/2(a1+an) Sequence a1,a2,a3,…….an Sum of an Infinite Geometric Series S=Ea1r^i=a1/1-r nth Term of a Geometric Sequence an=a1r^n-1 Sum of Fourth Power of Integers n(n+1)(2n+1)(3n^2+3n-1)/30 nth Term of an Arithmetic Sequence an=dn+c OR an=a1+(n-1)d Sum of the Fifth Power of Integers n^2(n+1)^2(2n^2+2n-1)/12 Common Difference : Common Ratio […]

standard equation of a circle with center (h,k) and radius r The Distance Formula point-slope form for the equation of a line average rate of change from (x₁,y₁) to (x₂,y₂) another name for slope How to evaluate (f+g)(x) To evaluate what? How to evaluate (f-g)(x) To evaluate what? How to evaluate (fg)(x) To evaluate what? […]

linear function y=mx+b constant function y=b identity function f(x)=x absolute value function f(x)=|x| quadratic function x^2 cube function x^3 square root function f(x)=√x cube root function f(x)=^3√x reciprocal functin 1/x vertical stretch a•f(x) changed by a factor of \”a\”, if a>1 vertically shrunk a•f(x) changed by a factor of \”a\”, if <0a<1 horizontally shrunk f(ax) […]