Quadratic Formula

If the discriminate is negative, how many real solution(s) will there be?

0

The radicand in the quadratic formula is called the

discriminate

If the discriminate is zero the solution(s) will be ___ number(s).

1 rational

If the discriminate is positive but not a perfect square the solution(s) will be ___ number(s).

2 irrational

If the discriminate is positive and also a perfect square the solution(s) will be ___ numbers(s).

2 rational

Mrs. Breland

My favorite teacher

In the quadratic formula, the coefficient of the squared term is

a

In the quadratic formula, the coefficient of the linear term is

b

In the quadratic formula, the constant is

c

Graphing Method

graph the equation and the solution is the x-intercept, where the parabola meets or crosses the x-axis

If the discriminant is positive,

it has two solutions

If the discriminant is 0,

it only has one solution.

How do you find the solution to a system of nonlinear equations?

look at the points where they cross each other

Mrs. Breland's favorite color

pink

Quadratic Formula Method

plug in a, b, and c into the quadratic formula and solve

To use the quadratic formula we must first write the quadratic in ___ form.

standard

Solve 2x²-3x+2=0 using the Quadratic Formula.

x=(3±i√7) / 4

Solve 2x²-3x+2=0 using the Quadratic Formula.

x=(3±√-7) / 4

Solve x²-3x-5=0 using the Quadratic Formula.

x=(3±√29) / 2

Solve 2x²-7x-1=0 using the Quadratic Formula.

x=(7±√57) / 4

Solve x²+4x+2=0 using the Quadratic Formula.

x=-2±√2

Solve 2x²+3x-5=0 using the Quadratic Formula.

x=1 or x=-2.5

Solve 4x²-5=0 using the Quadratic Formula.

x=±√5 / 2

Completing the Square Method

divide b by 2 and square it to find c, and then find the root

Factoring Method

find two numbers that multiply to get ac and add/subtract to get b, and then factor by grouping

If the discriminant is negative,

the answer is no solution.

Discriminant

the part of the quadratic equation which is located inside of the square root= b squared - 4ac

Square Root quadratic

when both sides of the quadratic equation are perfect squares, square root both sides and solve for x

Solve 2x²+x+5=0 using the Quadratic Formula.

x=(-1±i√39) / 4

Solve 4x²+x+5=0 using the Quadratic Formula.

x=(-1±i√79) / 8

Solve 4x²+x+5=0 using the Quadratic Formula.

x=(-1±√-79) / 8

Solve 6x²+x-3=0 using the Quadratic Formula.

x=(-1±√73) / 12

Solve 2x²+x+5=0 using the Quadratic Formula.

x=(-1√-39) / 4

Solve 2x²+6x-5=0 using the Quadratic Formula.

x=(-3±√19) / 2