Solving Quadratic Equations

Tammy WallaceVarina High

What is a Quadratic Equation?

A QUADRATIC EQUATION is an equation in which the greatest power of any variable is 2.

The standard form of a quadratic equation is , where a, b, and c are real numbers and a ≠ 0.𝑎𝑥2+𝑏𝑥+𝑐=0

Quadratic EquationsThe factors of a quadratic equation in standard from are related to the x-intercepts of the graph of its related function.

Therefore, you can find or confirm the factors of a polynomial by looking at the x-intercepts of the graph of its related function.

Factor . Then plot the x-intercepts using a calculator.There is no GCF so

continue with factoring the trinomial.

= 0

Use the graphing calculator to plot at least 4 points.

Where are the x-intercepts located?

(0, -5) and (0, 2)What is the relation between the factored form and the x-intercepts?

The factors, when solved for zero, give the location of the x-intercepts.

To find he solution to the quadratic equation, 1)factor, 2)set each factor equal to zero, then 3)solve each factor for x.

1) = 0

2) and

3) Solve each factor for 0 and

The factors, when solved for zero, give the location of the x-

intercepts.

+ 2 +2

- 5 -5

= 2

= -5

The solution to the quadratic equation is

Solving Quadratic Equations

Both methods, factoring and graphing, can be used to solve quadratic equations.

There several ways we can describe the solutions to quadratics. The following words may be used when asked to find the solution to a quadratic equation:

1. X-intercepts2. Solutions

3. Roots4. Zeros

Find the solution to by factoring and graphing.

= 0

and

and

−4−4 +1+1

Where are the x-intercepts located?

(0, -4) and (0, 1)

The solution is {-4, 1}

Find the solution to by graphing.

Where are the x-intercepts located?

(0, 5) and (0, 7)

What are the solutions?

{5, 7}

Find the solution to by factoring.

= 0

and

and

−5−5 −3−3

{-5, -3}

Given the solution, {-4, 2}, what is the quadratic

equation.Lets work backwards.

and

Therefore,

Multiply the binomials

+4 𝑥=2 -2

Given the graph, what is the quadratic equation.

Where are the solutions?

and

Therefore,

Multiply the binomials

+2 𝑥=3 -3

Where else can roots be found?

Roots, solutions, x-intercepts or zeros can also be found for linear equations.

To find the solution of a linear equation, set the equation equal to zero and solve for x. The answer also can be solved or verified by graphing as well.

Find the solution to by factoring and graphing.

= 0

and

and +2+2

The solution is

{2}