Recap: Solving Quadratic Equations-All Methods

Recap: Solving Quadratic Equations-All Methods

By Factoring (all terms are present)

• trinomial is factorable

• set equal to 0 before solving

• take GCF out (if there is a GCF)

• find factors using

   $a\cdot c$  

• set each factor equal to 0 and solve

Open Ended

Solve the quadratic equations by factoring:

 $3n^2+24n=-21$  

Open Ended

Solve the quadratic equations by factoring:

 $x^2=-10x-16$  

Open Ended

Solve the quadratic equations by factoring:

 $x^2=-10x-16$  

By Factoring (perfect square trinomial)

• do not set equation equal to 0

• factor the trinomial

• take the square root of both sides

• solve for x

Open Ended

Solve the quadratic equation by factoring:

 $4x^2+12x+9=81$  

By Factoring (c value is missing)

• set equation equal to 0

• take out GCF

• set both factors equal 0

• solve for x

Open Ended

Solve the quadratic equation by factoring:

 $3x^2=5x$  

By Taking Square Roots (b value is missing)

• do not set equal to 0

• isolate the square term

• divide by the coefficient of x², if any

• take square root of both sides

• solve for x

Open Ended

Solve by taking square roots:

 $2x^2-6=30$  

Solve by Completing the Square

• can be used with any quadratic trinomial

• set equation equal to the c value

• complete the square using (b/2)²

• factor the trinomial

• take the square root of both sides

• solve for x

Open Ended

Find the value of c that completes the square:

 $x^2-16x\ ...$  

Open Ended

Solve by completing the square:

 $x^2-10x+3=0$  

Open Ended

Solve by completing the square:

 $x^2+17x+44=x+4$  

Open Ended

Write the equation in vertex form:

 $y=x^2+10x+9$  

Solve using the Quadratic Formula

 $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  

• set up equation in standard form

• substitute a, b and c values into the formula

• solve for x

Open Ended

Solve using the Quadratic Formula:

 $2x^2-4x=-7$  

Open Ended

Determine the value of the discriminant, and the number and type of solutions:

 $4x^2-8x=3$  

Open Ended

Determine the value of the discriminant, and the number and type of solutions:

 $x^2-8x+16=0$