Interpreting Expressions (NC.M1.A-SSE.1A)
In the expression 5x+7, this is the name for '5'.
What is a coefficient?
In the expression 10x+5, representing the total cost of renting a bike for x hours, this number represents the hourly rental rate.
What is 10?
The factored form of 2x+6.
What is 2(x+3)?
The sum of (3x+2)+(x−5).
What is 4x−3?
If (x−4) is a factor of a polynomial, this is one of its zeros.
What is x=4?
The individual parts of an expression that are separated by addition or subtraction signs, such as 3x2, −2x, and 4 in 3x2−2x+4.
What are terms?
If a car's value is modeled by V(t)=20000(0.85)t, where t is years, this number indicates the annual rate of depreciation.
What is 0.15 (or 15%)?
The product of (x+4)(x−4).
What is x2−16?
The result of subtracting (x2+3x) from (4x2−x).
What is 3x2−4x?
The zeros of the function f(x)=(x−5)(x+1).
What are x=5 and x=−1?
In the expression (x+2)(x−3), these are the two quantities being multiplied.
What are factors?
For the function h(t)=−16t2+60t+5, which models the height of a projectile, this term represents the initial height from which the projectile was launched.
What is 5 (or the constant term)?
The factored form of the quadratic expression x2+5x+6.
What is (x+2)(x+3)?
The product of x(x+7).
What is x2+7x?
The graph of a polynomial crosses or touches the x-axis at these points.
What are the zeros, solutions (or x-intercepts)?
For the expression 2(x+y), this property allows us to write it as 2x+2y.
What is the distributive property?
n the cost function C(x)=25+0.50x, where x is the number of items produced, this value represents the fixed cost (cost incurred even if no items are produced).
What is 25?
To show the zeros of a quadratic function like f(x)=x2−4x+3, you would rewrite it in this factored form.
What is f(x)=(x−1)(x−3)?
The product of (x+3)(x−2).
What is x2+x−6?
To find the zeros of f(x)=x2−9, you would set the expression equal to zero and then factor it, resulting in these two values.
What are x=3 and x=−3?
In the expression P(1+r)t, this variable represents the initial principal amount.
What is P?
If a population doubles every year, modeled by P(t)=P0(2)t, this number represents the growth factor per time period.
What is 2?
The equivalent exponential form of 23⋅25.
What is 28?
The result of (2x−1)(x2+3x−4).
What is 2x3+5x2−11x+4?
If the zeros of a quadratic function are x=0 and x=7, this is a possible factored form of the function.
What is f(x)=x(x−7) (or f(x)=k⋅x(x−7) for any non-zero constant k)?