The last bit of new material for this unit takes us back to the connection between the roots/solutions of a quadratic and the x-intercepts of its graph. This relationship exists even with polynomials of higher degrees, which means we can use that relationship to factor using its roots! We introduced two tasks today:

• Using the known roots of a polynomial to write the polynomial, and
• Using the graphing calculator to find the zeroes, and by extension the factors, of the polynomial.

These are the last two new items, in addition to everything else you’ve learned this unit, that will appear on your Unit 3 test on Tuesday, December 18.

Today’s Files

• HW 3.17 – Using Roots to Factor
• Notes
• Lesson Video 1 (finding a polynomial from its zeroes)
• Lesson Video 2 (using roots of a polynomial to factor)
• Video Archive
  • Review of key features of parabolas
  • Finding key features with graphing calculator
  • Solving a quadratic equation by factoring
  • Solving a quadratic equation with quadratic formula
  • Simplifying radicals
  • Solving a quadratic equation with the square root
  • Area word problems
  • Finding axis of symmetry algebraically

Cumulative IXL Modules

• J.4 Solve a quadratic equation using square roots
• J.5 Solve a quadratic equation using the zero product property
• J.6 Solve a quadratic equation by factoring
• J.9 Solve a quadratic equation using the quadratic formula
• L.1 Roots of integers
• L.2 Roots of rational numbers
• L.3 Find roots using a calculator
• L.7 Multiply radical expressions
• T.1 Identify the direction a parabola opens
• T.2 Find the vertex of a parabola
• T.4 Find the axis of symmetry of a parabola
• From Algebra 1
  • F.3 Area and perimeter: word problems
  • BB.1 Characteristics of quadratic functions
  • EE.1 Simplify radical expressions