Quadratics Review

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

• x = -2 ± √3

• x = -3 ± √2

• x = 2 ± √3

• x = 2 ± √2

Solve
4m² - 100 = 0

• m=25, -25
• m=96
• m=5, -5
• m=-96

Solve
a² + 2a - 24 = 0

• a = -6, 4
• a = 6, -4
• a = 12, -2
• a = 8, -3

Factor:

x² + 11x + 24

• (x + 6)(x + 4)

• (x + 12)(x + 2)

• (x - 8)(x - 3)

• (x + 8)(x + 3)

Here is the graph of $y=x^2+11x+24$ .

In factored form, it was 
 $y=\left(x+3\right)\left(x+8\right)$ .

What do you notice about the factors compared to the x-intercepts of the equation?

What are the factors of 3x²-17x+10

• (x-5)(3x-2)
• (x+5)(3x+2)
• (3x-5)(x-2)
• (x+5)(3x-2)

Here is the graph of $y=3x^2-17x+10$ .

In factored form, it was y=(3x-2)(x-5)

What do you notice about the factors compared to the zeros of the graph?

Here is the graph of $y=5x^2+20x+20$ .

In factored form, it was  $y=5(x+2)^2$ .

What do you noticed about the factors compared to the zeros of the graph?

What are the zeros?

• x= 0 and x= -4
• x= 0 and x= 4
• y= 0
• x= 2

Solve by taking square roots:
k² - 6 = 43

• k = √37
• k = 37 or - 37
• k = 7, k = -7
• no solution