Martin Gay Intermediate Algebra Answer Key - Practice-Ready Answer Guide
Martin Gay Intermediate Algebra Answer Key - Practice-Ready Answer Guide linear function equation - answer - y=x y=x+1 quadratic function equation - answer - y=x²-2 absolute function - answer - y=|x| how to determine if a graph is a valid function? - answer - vertical line test line can only pass through one point on the graph linear function in slope-intercept form - answer - y=mx+b linear function in point-slope form - answer - y-y₁=m(x-x₁) what is the shift in f(x)=|x-1|? - answer - shifts across the x-axis, positive (because absolute function), shifts 1 unit to the right quadratic functions - answer - ax²+bx+c=0 **constant term is always y-intercept what is the domain and range of a linear equation? - answer - D=all real numbers R= all real numbers what is the shift of y=f(x+1)-2? - answer - 1 unit left 2 units down what is the domain of a number with an odd root? (ex: cubic root) - answer - D=all real numbers quadratic formula - answer - x=-b±√b²-4ac/2a distance formula - answer - d=√(x₁-x₂)²+(y₁-y₂)² geometric sequences have - answer - common ratio arithmetic sequences have - answer - common difference recursion formula - answer - a∨n=2+a∨(n-1) general terms (geometric sequence) - answer - a∨n=a₁×rⁿ⁻¹ how to find # of terms in an arithmetic sequence - answer - (last term-first term/d)+1 midpoint formula - answer - (x₁+x₂/2, y₁+y₂/2) equation of a circle - answer - r²=(x-h)²-(y-k)² if center is (0,0): r²=x²+y² equation of an ellipse - answer - y²/a² + x²/b² = 1 MUST ALWAYS EQUAL 1!!! equation of HORIZONTAL & VERTICAL ellipses - answer - horizontal: (x-h)²/a² + (y-k)²/b² = 1 vertical: (y-k)²/a² + (x-h)²/b² = 1 completing the square - answer - add the result of (b/2)² to both sides of the euqtion (to get equation into standard form) COEFFICIENT OF x² & y² MUST BE 1!!! equation of a hyperbola - answer - x²/a² - y²/b² = 1 WHICHEVER TERM IS POSITIVE DETERMINES IF HORIZ/VERT if x is positive, horizontal if y is positive, vertical
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