Unit 3 - algebra 1

Question 1

How to complete the square + x^2 + 10x?

Answer 1

Put a quadratic formula into the format y(x+a)^2 -b
E.g. x^2 + 10x -> (x+5)^2 - 25

Question 2

What is the coefficient?

Answer 2

Number in front of something. E.g. 6x coefficient is 6.

Question 3

How to complete the square when the coefficient isn’t 1 + 2x^2 + 8x+7?

Answer 3

First factorize coefficient, than complete the square within brackets, expand outer bracket & simplify.
E.g. 2x^2 + 8x+7?
2(x^2+4x) +7
2((x+2)^2 -4) + 7
2(x+2) ^2 - 8 +7
2(x+2)^2 -1

Question 4

Why do we complete the square?

Answer 4

• solve for x/solving equations
• finding maximum/minimum point (turning point) of parabola. E.g. in (x-2)^2 +7 the turning point is 2 (a is made nagative and represents x) 7 (b represents y)
• y(x+a)^2 + b

Question 5

What is the quadratic formula?

Answer 5

In the form of ax^2 + bx + c
-b +- root b^2 -4ac/2a

Question 6

How to split the middle + 2x^2 + 8x + 8?

Answer 6

1. In the form of ax^2 + bx + c, find what 2 numbers add to b and multiply to ac
2. Split the x values
3. Factorize
   E.g. 2x^2 + 8x + 8
   b = 8, ac = 16. 4 and 4 add to 8 and multiply to 16.
   2x^2 + 4x + 4x + 8 = 2x(x+2) + 4(x+2) = (2x+4)(x+2)

Question 7

How do we find the solutions for x when splitting the middle + (x-2)(x-3)?

Answer 7

Number in each bracket but negative. If coefficient of x isn’t 1, divide the number by coefficient.
E.g. (x-2)(x-3) - x can be 2 or 3.