Quadratic and Vertex

Factor x² - 8x + 16

Answer explanation

To factor x² - 8x + 16, we look for two identical numbers that multiply to 16 and add to -8. The numbers -4 and -4 fit this, so the expression factors to (x-4)(x-4), which is also written as (x-4)².

Factor the following expression: x² + 18x + 81

Answer explanation

To factor x² + 18x + 81, we look for two numbers that multiply to 81 and add to 18. The numbers 9 and 9 fit this, so we can write the expression as (x+9)(x+9) or (x+9)².

Solve the following equation by Factoring: 3x² − 7x − 40 = 0

Answer explanation

To factor 3x² - 7x - 40, we look for two numbers that multiply to -120 (3*-40) and add to -7. The numbers -15 and 8 work. Thus, we can factor it as (3x + 8)(x - 5) = 0. Setting each factor to zero gives x = 5 and x = -8/3.

Solve the equation from last question (x² +4x +5 = 0) by quadratic formula

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Answer explanation

To solve x² + 4x + 5 = 0 using the quadratic formula x = (-b ± √(b² - 4ac)) / 2a, where a=1, b=4, c=5. Calculate the discriminant: 4² - 4(1)(5) = 16 - 20 = -4. Since it's negative, there are no real solutions.

Graph y = x² + 6x + 5 On your sketch, find out the vetex point, x-intercept(s) and y-intercept.

Find the discriminant (b² - 4ac) for equation: x² + 4x + 5 = 0 _

How many real number solutions do we have? _

Answer explanation

To find the discriminant, calculate b² - 4ac. Here, a=1, b=4, c=5. Thus, the discriminant is 4² - 4(1)(5) = 16 - 20 = -4. Since the discriminant is negative, there are 0 real number solutions.

Sketch y = -2 (X +1)² +3

What is the vertex for
f(x)=4(x-2)² + 3

• (-2, 3)

• (2,-3)

• (4,3)

• (2,3)

What is the axis of symmetry for 
f(x)=4(x-2)² + 3

• 4

• 2

• x = -2

• x = 2

What is the vertex of the parabola: y=2(x-3)²+4

• (3,4)

• (-3,4)

• (3, -4)

• (-3,-4)