Quadratic equations & quadratic formula

A flashcard set on quadratic equations/formula.

What is a quadratic?

A polynomial with a degree of 2

What is a quadratic equation?

An equation in the form ax²+bx+c, where a≠0, x is a variable and a,b and c are constants. In other words, it is an equation where the highest power of the variable (usually x ) is 2 .

What is a radical?

The √ symbol that is used to denote/show the square root

There are three main ways to solve a quadratic equations. The ______ formula, _____ and ______

Quadratic, inverse operations, radicals, Factoring

Why use the quadratic formula?

The quadratic formula is a guaranteed way to solve or fact check quadratic equations.

Before using the quadratic formula make sure the equation is simplified to what form?

ax²+bx+c=0

Simplfiy 3x²+6x=-10 so you can use the quadratic formula.

3x²+6x=-10

+10 +10

3x²+6x+10=0

What do the letters a,b,c represent in the quadratic formula?

The numbers in a quadratic equation like so:

ax²+bx+c=0

If ax²+bx+c=0 is the equation for a quadratic than what does a,b and c equal for

x²+4y-21=0

a=1 b=4 c=-21

What is the quadratic formula?

x=(-b±√(b²-4ac))/(2a)

Solve x²+4xy-21=0 using the quadratic formula

x=-2±5

Solve 3x²+6x=-10 using the quadratic formula

-6±√-84/6

No real solution, the radical number is negitive

What do you when when you get numbers like √50 that cant be squared?

Factor out the largest perfect square. (Can help by dividing my 2 or 4 just make sure it makes one square number)

In this example that would be 25 (5×5)

Since it is a factor, put that factor in the √

√25×2

Remember: √axb= √a x √b

√25 x √2 Simplfy

5√2

Simplfy √24

√4 is a perfect square

√4 × 6

√4 x √6

2√6

Simplfy √18

√9 is a perfect square

√9 × 2

√9 x √2

3√2

Simplfy √20

√4 is a perfect square

√4 × 5

√4 x √5

2√5

What is √8 ?

2√2

√a⋅b= ____

√a⋅√b

What is a perfect square?

A number that is achieved by squaring (multiplying by itself) another integer. ex: 9 is a perfect square because 9 = 3²

All intergers in a square root must be ___ ____ to result in a whole number.

perfect squares

Solve 3d²-8d+3=0 using the quadratic form (or algebraically), rounding to the nearest hundredth

d=0.5,2.2

Use the quadratic formula to solve x²-4x+1=0 for x.

Round the answers to the nearest hundredth

x= 3.72,0.27

Solve x²-9x=36 algebraically (quadratic formula) for all values of x

x=12,-3

Solve x²+3x-9=0 algebraically (quadratic formal) for all values of x. Round to the nearest hundredth

x=1.85,-4.85

Using the quadratic formula solve 3x²-2x-6=0 for all values of x. round up to the nearest hundredth.

x=1.79,1.12

What does it mean to express in the simplest radical form?

The farthest you can go with the quadratic formula while still having the √ symbol.

Use the quadratic formula to solve the equation 3x²-10x+5=0. Express the answer in simplest radical form.

x= 10x±2√10 / 6

How do you determine the exact roots (answers) of an equation using the quadratic formula?

solve regularly than before dividing, and then make two equations from the ±. ex:

If b²-4ac = 0 there are ____ real solutions

one

If b²-4ac > 0 there are ____ real solutions

two real solutions

If b²-4ac < 0 there are ____ real solutions

zero