Polynomials and Quadratics

Question 1

How do you find the equation of a tangent to a curve?

Answer 1

Coordinate - sub the x-value into the equation

Gradient - sub the x-value into the derivative

Then use y-b=m(x-a)

Question 2

What must you always include in your answer to a quadratic inequality question?

i.e. x^2+4x+3 > 0

Answer 2

A sketch showing where your answers lie

i.e. for x^2+4x+3 > 0

(x+3)(x+1)

x < -3 or x > -1

Question 3

How do you show something is a factor (or a root) of a polynomial?

Answer 3

Do synthetic long division and show he remainder = 0 then say so

i.e. “reminder = 0 therefore (x-1) is a factor.”

Question 4

How do you find the gradient of a tangent to a curve?

Answer 4

Differentiate the equation of the curve then substitute the x-coordinate into the derivative.

Question 5

How do you ‘complete the square’ when there is a non-unitary coefficient of x^2?

Answer 5

(1) Factorise the first 2 terms only by taking out the x^2 coefficient.
(2) Complete the square on the x^2 and x terms only.
(3) Expand out the bracket then tidy up.

Question 6

How do you complete the square and why do we do it?

Answer 6

Always the start with the ‘blank template’ -
(x )^2-

Then half, square, drop down and tidy up

Question 7

How do we find the stationary points of a function?

Answer 7

Differentiate the function then set the derivative to 0 and solve it.

(As the gradient of tangent at stationary points is 0)

Question 8

How do we find where a line or curve meet another curve or line? (If at all)

i.e. points of interesection

Answer 8

Make the same term equal to each other (usually y=y but doesn’t have to be)

Or simultaneously equate the equations.