April 23, 2015

Students rewrite quadratic expressions given in standard form, ax2 + bx + c (with a ? 1), as equivalent expressions in completed square form, a(x - h)2 + k. They build quadratic expressions in basic business application contexts and rewrite them in equivalent forms.

Teacher and Student versions of full lesson from engageNY

- Mathematics > General
- Mathematics > Algebra

- Grade 9
- Grade 10

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity.

Factor a quadratic expression to reveal the zeros of the function it defines.

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

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. Derive the quadratic formula from this form.

Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.