Quadratics (equations, graphs, inequalities)

Question 1

What is the quadratic formula?

Answer 1

x=-b±√(b²-4ac))/2a

Question 2

When do we use the quadratic formula?

Answer 2

When it states in a question to give your value of x or solutions of x to any significant figure or decimal place.

Question 3

When do we use ‘completing the square’ method in quadratics?

Answer 3

When your question looks like this:
Solve x^2+6x+7=0
Give your answer in the form a±√b where a and b are INTEGERS.

If the equation at the top doesn’t equal 0 then rearrange to equal 0.

Question 4

What does the ‘completed square form’ look like?

Answer 4

(x+a)^2 - b

Question 5

What does a quadratic equation look like?

Answer 5

ax^2 + bx + c = 0

Question 6

What is a coefficient?

Answer 6

The number that goes in front of and multiplies an algebraic expression. e.g. 4 in 4x.

Question 7

How would you ‘Express x^2 +4x -3 in the form (x+a)^2-b where a and b are integers’? (completing the square)

Answer 7

Step 1- Write your brackets
(x+2)^2
a is half of the number in front of x (4/2=2)
Step 2- Minus the number you don’t want (4)
If we expand those brackets we will have x^2 +4x + 4 and we don’t want the ‘4’ on the end
(x+2)^2 -4
Now this equation is equal to x^2+4x.
Step 3- Add the number you want (-3)
(x+2)^2-4-3
Step 4- Then simplify the subtractions
(x+2)^2-7

Question 8

What is the general equation for a quadratic graph? (curved graph)

Answer 8

y=ax^2 +bx +c

They can have other equations such as:
y=x^2
y=-x^2
f(x)=1+4x-x^2
f(x)=(x+3)(x-7)