Central High A1.FIF.8* Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function. (Limit to linear; quadratic; exponential.) (Note: A1.FIF.8a is not a Graduation Standard.) a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret o Identify the point-slope form of a linear function as 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1). o Identify the slope-intercept form of a linear function as 𝑓(𝑥) = 𝑚𝑥 + 𝑏. o Identify the standard form of a linear function as 𝐴𝑥 + 𝐵𝑦 = 𝐶. o Use definitions of 𝑥-intercept and 𝑦-intercept to find the intercepts of a standard form line. o Relate the constants 𝐴, 𝐵, and 𝐶 to the values of the 𝑥-intercept, 𝑦-intercept, and slope. o Compare the relationship between quantities using equations, verbal descriptions, graphs, and tables of the same function. For FIF.8a: o Explain that there are three forms of quadratic functions: standard form, vertex form, and factored form. o Explain that standard form is f(x) = ax2+bx+c. o Explain that the vertex form is f(x) = a(x-h)2+k. o Explain that factored form is f(x) = a(x - x1)(x - x2). o Explain that the graph of all three forms is a parabola. o Explain that all parabolas can be written in standard and vertex form, but that parabolas without x-intercepts cannot be expressed Algebra 1 22 these in terms of a context. in factored form using real numbers. (Parabolas without xintercepts can be expressed in factored form using complex numbers not encountered in Algebra 1.) o Find the x-intercepts of a quadratic written in factored form. o Use the x-intercepts of a quadratic function to find the axis of symmetry. o Use the axis of symmetry of a quadratic to find the vertex of a parabola. o Identify the line of symmetry and vertex of a quadratic written in vertex form. o Sketch the graph of a parabola written in vertex form. o Determine if a quadratic written in vertex form has x-intercepts by looking at the equation.