1.1 Quadratics

[ PURE 1 ] 1) Solving Quadratic equations 2) Quadratic Inequalities 3) Completing the square 4)Nature of the roots

In the equation, what is the value of a

a = -1

In the equation what is the value of b

b = (4+m)

In the equation what is the value of c

c = 13

What are the different methods of solving a quadratic?

1. Factoring middle term
2. Quadratic formula
3. Calculator method

How do you solve the equation

Take u = x^2 and u^2 = x^6

x=0.87358 and x=-1.4422

Solve the equation

Take

3^x = u

3^2x = u^2

(3^2)^x = u^2

9^x = u^2

What are the values of x called?

The x-intercepts

1 Shaded area is equal to ______

1 answer

2 shaded areas are equal to ______

2 answers

Solve the Quadratic Inequality

Solve the Quadratic Inequality

Complete the square

What is the Discriminant?

When the roots are real and distinct

OR

The line intersects the curve at two points

Value will always be positive

When the roots are real and equal (one real root)

OR

The line is a tangent to the curve

No real root

OR

The line does not intersect the curve

OR

The curve is above the x-axis

Value will always be negative

The roots are real

OR

The line intersects the curve

(Does not mention how many times it touches the curve)

k = -9 and k = -5