Solving Quadratics-Choosing a Strategy

Solving Quadratics-Choosing a Strategy

Learning Target: I can choose the most efficient method to solve quadratics

Methods to Solve Quadratics

• Zero Product Property (area model & diamond)

• Complete the square (rewrite into perfect square form)

• Quadratic formula (evaluate with a, b, and c values)

Poll

Which method are you MOST confident with?

• Factoring

• Complete the Square

• The Quadratic Formula

Poll

Which method are you LEAST confident with?

• Factoring

• Complete the Square

• The Quadratic Formula

Multiple Choice

Which option shows what quadratics in standard form look like?

• $y=ax\ +bx^2+c$

• $y=ax^2+bx+c$

• $y=a\ +bx+cx^2$

• $y=ax^2+b+cx$

Zero Product Property

• Must equal 0

• Works for SOME quadratics

• Use when numbers are the smaller & easily factorable

Multiple Choice

Use Zero Product Property to solve

x² + 2x - 15 = 0

• x = 3 or x = 5

• x = 5 or x = -3

• x = -5 or x = 3

• x = -3 or x = -5

Complete the Square

• Use this when a, the coefficient of x² , is 1

• Best when b, the coefficient of x, is even

Multiple Choice

What should be added to both sides of the following equation to complete the square?
x² + 12x = 5

• 12
• 6
• 36
• 5

The Quadratic Formula

•  $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  

• Works for ALL quadratics

• Great for quadratics with large coefficients

• Must equal 0

Multiple Choice

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

• a = 4, b = -8, c = 3

• a = 4, b =-8, c =-3

• a = 4, b = 8, c = 3

• a = 4, b = 8, c = -3

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

Poll

Decide on the best method:

x² - 3x - 54 = 0

• Factoring

• Complete the Square

• The Quadratic Formula

Poll

Decide on the best method:

x² + 2x = -9

• Factoring

• Complete the Square

• The Quadratic Formula

Poll

Decide on the best method:

3x² + 13x = -4

• Factoring

• Complete the Square

• The Quadratic Formula

Poll

Decide on the best method:

4x² + 12x + 9 = 81

• Factoring

• Complete the Square

• The Quadratic Formula