Solving Quadratics

Solutions-Oriented(The Discriminant)

100

What is the discriminant?

b^2-4ac

It is the value that tells us how many and what type of solutions a quadratic equation can have. You can find it under the radical in the quadratic formula (on the reference sheet).

If the discriminant is 0, there will be 1 root. If the discriminant is >0, there will be 2 roots. If the discriminant is <0, there will be no real roots.

200

Which graph represents a quadratic function with a discriminant of 4?

Graph 3.

It has two real roots (touches the x-axis once), which means it has a discriminant greater than 0.

What’s the x-"Factor"?(Solve by Factoring)

100

Solve the following quadratic equation by factoring.

n^2-7n+6=0

{6, 1}

200

Solve the following quadratic equation by factoring:

5n^2+41n-12=-4+2n

{1/5, -8}

Don’t be a square!(Solve by CTS/Square Roots)

100

Use the square root method to determine the values of x for the equation

9x^2-81=0

{+-3}

200

Use the method of completing the square to determine the values of x for the equation

x^2-2x=24

{-4,6}

The Plus-Minus Side(Solve by Quadratic Formula)

100

Use the quadratic formula to find the exact roots of  4x^2-17x=-12 .

200

Use the quadratic formula to find the roots of x^2-9x+6=0 . Round the solutions to the nearest hundredth.

{0.73, 8.27}