4) Quadratics

Question 1

How do you complete the square in a quadratic equation?

Answer 1

ax'+bx+c  ('=square)
1. Take out the coefficient of x as a factor (unless it is 1) for the first two terms. e.g. 2x'+10x+7=2(x'+5x)+7
2. Ensure x isn't squared inside the bracket and half B.
2x'+10x= 2(x+5/2)'-25/4
3.Then add c and simplify.
so 2x'+10x+7=2(x'+5x)+7
=2{(x+5/2)'-25/4} +7
      25/4 * 2= 25/2
=2(x+5/2)'-25/2 +7
=2(x+5/2)'-11/2

Question 2

What do I use completing the square for?

Answer 2

1) To find the axis of symmetry ( which means what does y equal)
2)the vertex of a graph (the highest or lowest point in the parabla ( the shape a quadratic expression makes in a graph), hint it is a coordinate)
e.g.
1)y= x’+10x+32
y={(x+5),-25}+32
y= (x+5)’+7
2) y= 7 and x= -5 so ans is the coordinate (-5,7)

Question 3

What are coefficients of x’ and x in a quadratic equation?

Answer 3

a and b in that order

Question 4

What is c often called in a quadratic expression?

Answer 4

the constant term

Question 5

What two forms can you write a quadratic expression in?

Answer 5

1) factor form e.g. (x+4) (x-3)

2) completed square form e.g. (x+2)’-5

Question 6

Why doesn’t quadratics factorize if they r the sum of 2 squares?

Answer 6

ax^2 +c, is always equal to or greater then +c as x is greater than or equal to 0, therefore if it did have facotrs (x-p)(x+q) it would equal 0 when x=p or x=q however the equation cannot equal 0 therefore it doesn’t factorise

Question 7

What would you do for the question type: Find where the quadratic y=(2x-1)(x-2) meets the x-axis

Answer 7

1) Ensure y is on its own
2) solve the equation
3) right the 2 coordinates ( if theres 2 roots) where y= always =0 and x =one of the answers

Question 8

How do you solve a quadratic equation if there is no constant term? (no c)

Answer 8

take out the factor x

https://www.youtube.com/watch?v=j3OUjxQhKLM

Question 9

1) How do you solve a quadratic equation using difference of 2 squares?
2) Also, How do you know you should be using the difference of 2 squares?

Answer 9

1)Square root the equation
e.g. x’-p’=(x+p)(x-p)
2) the coefficient of x = 0 , so b=0, and the constant
= -interger

Question 10

How can you reduce the time it takes to factorize quadratics where a, b and c equal a number.

Answer 10

By not working out possibilities where a factor (usually is a factor in other possibilities as well) doesn’t divide into the original quadratic.

Question 11

How would you use completing the square to solve the equation(find x)?

Answer 11

1) complete the square
2) ensure it equals 0
3) remove a, then c from both sides
4) square root, you’ll get 2 answers cos it can be + or -
5) state x= this and x=that

Question 12

Why do you use the discriminate and what is it?

Answer 12

to categorize what type of solution you will get discriminate= b’-4ac

Question 13

If the discriminant=
a) 0
b) perfect squared number
c) 0
what does it mean.

Answer 13

a) repeated root
b) 2 roots
c) 2 roots
c) no real roots

Question 14

add example 4.6.3-4 p 65

Answer 14

iubf

Question 15

4.7.3 At how many points does the line x+2y=3 meet the curve 2x^2+y^2=4

Answer 15

1) substitute x in so you only have one unknown
2) reduce the equation (simplify) this will mean you have it in the form ay^2+by+c=0
3) use the desciminate to find the no. of roots
4) the no. of roots = the no. of points of intersection

Question 16

What do you do to solve t^4+13t^2+36=0

Answer 16

1) say t^4=t^2 or sqrt of t =t
2) solve
3) undo first step (remember you can’t square root a negative integer so = nothing)