Standard(s):
[MA2019] ACC-8 (8) 4 : 4. Interpret linear, quadratic, and exponential expressions in terms of a context by viewing one or more of their parts as a single entity. [Algebra I with Probability, 4]
Example: Interpret the accrued amount of investment P(1 + r)t , where P is the principal and r is the interest rate, as the product of P and a factor depending on time t.
[MA2019] ACC-8 (8) 6 : 6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.
b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.
c. Use the properties of exponents to transform expressions for exponential functions. [Algebra I with Probability, 6]
Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, or y = (1.2)t/10, and classify them as representing exponential growth or decay.
[MA2019] ACC-8 (8) 11 : 11. Select an appropriate method to solve a quadratic equation in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Explain how the quadratic formula is derived from this form.
b. Solve quadratic equations by inspection (such as x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real. [Algebra I with Probability, 9]
[MA2019] AL1-19 (9-12) 4 : 4. Interpret linear, quadratic, and exponential expressions in terms of a context by viewing one or more of their parts as a single entity.
Example: Interpret the accrued amount of investment P(1 + r)t , where P is the principal and r is the interest rate, as the product of P and a factor depending on time t.
[MA2019] AL1-19 (9-12) 6 : 6. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
a. Factor quadratic expressions with leading coefficients of one, and use the factored form to reveal the zeros of the function it defines.
b. Use the vertex form of a quadratic expression to reveal the maximum or minimum value and the axis of symmetry of the function it defines; complete the square to find the vertex form of quadratics with a leading coefficient of one.
c. Use the properties of exponents to transform expressions for exponential functions.
Example: Identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
[MA2019] AL1-19 (9-12) 9 : 9. Select an appropriate method to solve a quadratic equation in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Explain how the quadratic formula is derived from this form.
b. Solve quadratic equations by inspection (such as x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.
