Solving Quadratics by Completing the Square & Quadratic Formula

SOLVING QUADRATIC EQUATIONS BY
COMPLETING THE SQUARE &
THE QUADRATIC FORMULA

Dr. Tom Giles

SOLVING QUADRATIC EQUATIONS
like we did last week

Factoring

Factoring using a GCF

(Greatest Common Factor)

Multiple Choice

Factor by using GCF:
8n³ + 2n²

• 2n²(4n-1)
• 2n²(4n + 1)
• n²(8n+2)
• 3n(4n+1)

Multiple Choice

Factor by using GCF:
$$4x^3+16$$

• 2x²(4x-1)

• 4x(x + 4)

• x²(8x+2)

• 3x(4x+1)

Multiple Choice

Factor by using GCF:
8n³ + 2n²

• 2n²(4n-1)
• 2n²(4n + 1)
• n²(8n+2)
• 3n(4n+1)

Multiple Choice

Factor by using GCF:
$$4x^3+16$$

• 2x²(4x-1)

• 4x(x + 4)

• x²(8x+2)

• 3x(4x+1)

Trinomial Factoring

Trinomial Factoring

Multiple Choice

Factor:
x² + 7x - 30

• (x + 10)(x - 7)
• (x - 10)(x + 3)
• (x + 10)(x + 3)
• (x + 10)(x - 3)

Multiple Choice

Factor
n² + 5n - 6

• (n - 2)(n - 3)
• (n - 1)(n + 6)
• (n + 1)(n - 6)
• (n + 2)(n - 3)

Multiple Choice

Factor
x² + 9x - 36

• (x + 12)(x - 3)
• (x + 9)(x - 4)
• (x - 12)(x + 3)
• (x - 9)(x - 4)

Factoring Completely

Sometimes you have to find a GCF first, then factor again.

Multiple Choice

50m³ - 2m 

• 2m(25m²-1)
• 2m(5m-1) (5m-1)
• 2m(5m-1) (5m+1)
• PRIME

Multiple Choice

3x³ + 15x² + 18x

• 3x(3x + 9)(x - 15)

• 3x(x+3)(x+2)

• x(x - 5)(x + 5)

• 3x(x-3)(x - 3)

Multiple Choice

5m² -20m - 25

• 5(m+1) (m-5)

• (3m-5) (5m+5)
• 5(3m²-2m-5)
• PRIME

SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

Let's try together

Multiple Choice

What do you do to the b value to correctly complete the square?

Multiple Choice

When do you use the plus or minus symbol?

Multiple Choice

Complete the square for

x² + 12x + ____

• x² + 12x + 144

• x² + 12x + 36

• x² + 12x - 36

• x² + +12x - 144

Multiple Choice

Answer the question.

Multiple Choice

What is the first step in solving this equation

Multiple Choice

What do you need to add to both sides to complete the square?

• 6

• 36

• 10

• 144

Multiple Choice

When factoring x² -4x+4=0. What goes in the blank?

(x-_____)²=0

• 8

• 2

• 4

• 20

Multiple Choice

Solve the following equation by completing the square.

x²-2x-3=0

• {8,-7}

• {4,-4}

• {5,-3}

• {3,-1}

Multiple Choice

solve the quadratic equation by completing the square.

x²-2x-48=0

• {-6,-8}

• {6,8}

• {-6,8}

• {6,-8}

Multiple Choice

Solve the equation by completing the square.

x²-8x-9=0

• {-3,-13}

• {3,13}

• {-1,9}

• {1,9}

Multiple Choice

Solve the quadratic equations by completing the square.

5x²+50x+80=0

• {4,-14}

• {-4,-14}

• {-4,14}

• {4,14}

SOLVING QUADRATIC EQUATIONS BY the quadratic formula

Multiple Choice

Which is the general form of a quadratic equation?

• $$y=mx+b$$

• $$ax^2+bx+c=0$$

• $$\left(x-a\right)\left(x-b\right)=0$$

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

We will need the general form in order to use the quadratic formula

Example

Example

Multiple Choice

Use the quadratic formula to solve 2x² + 2x - 12?

• x = -2, 3

• x = 2, 3

• x = 2, -3

• x = -2, -3

Multiple Choice

Solve using the quadratic formula.
$$2x^2-9x-35=0$$  

• $$x=\frac{7}{2},\ x=-6$$  

• $$x=-\frac{5}{2},\ x=5$$  

• $$x=-\frac{3}{7},\ x=6$$  

• $$x=-\frac{5}{2},\ x=7$$  

Multiple Choice

Solve $$2x2+7x-15=0$$  

• x = -1.5 or 5

• No Solution

• x = -5 or 1.5

• x = 0.7 or 5

Example with a Complex Solution

We will use this to determine how many solutions a quadratic has!

Multiple Choice

Use the discriminant to determine the number of solutions for: $$x^2-x+2=0$$  

• 2 real soltuions

• 2 complex solutions

• 1 real solution

• no solution

Multiple Choice

Use the discriminant to determine the number of solutions for: $$2x^2-3x-2=0$$  

• 2 real solutions

• 2 complex solutions

• 1 real solution

Multiple Choice

Use the discriminant to determine the number of solutions for: $$x^2-2x+1=0$$  

• 2 real solutions

• 2 complex solutions

• 1 real solution

Writing a Quadratic Equation given the Solutions

Write a quadratic equation that has the solutions x = 4 and x = -7

Multiple Choice

Given the zeros , what is the quadratic equation?

• y=x² +6x -8

• y=x² +6x +8

• y=x² -2x -8

• y=x² -2x +8

Multiple Choice

Given the zeros, what is the quadratic equation?

• y=3x² +10x +8

• y=2x² ++11x +8

• y=3x² +14x +8

• y=2x² +5x +8

Multiple Choice

Write a quadratic function with solutions of

$$2+3i$$  and  $$2-3i$$  

• $$h\left(x\right)=x^2-4x-6$$  

• $$p\left(x\right)=x^2-4x-6$$  

• $$k\left(x\right)=x^2-4x+13$$  

• $$f\left(x\right)=x^2+4x+13$$  

Poll

What is your favorite way of solving quadratic equations so far?!

• Factoring

• Square Root Property

• Completing the Square

• Quadratic Formula