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Solving Quadratic Equation by Graphing. Section 6.1. Quadratic Equation. y = ax 2 + bx + c ax 2 is the quadratic term. bx is the linear term. c is the constant term. The highest exponent is two; therefore, the degree is two. Identifying Terms. Example f(x)=5x 2 -7x+1

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quadratic equation
Quadratic Equation

y = ax2 + bx + c

ax2 is the quadratic term.

bx is the linear term.

c is the constant term.

The highest exponent is two; therefore, the degree is two.

identifying terms
Identifying Terms

Example f(x)=5x2-7x+1

Quadratic term 5x2

Linear term -7x

Constant term 1

identifying terms1
Identifying Terms

Example f(x) = 4x2 - 3

Quadratic term 4x2

Linear term 0

Constant term -3

identifying terms2
Identifying Terms

Now you try this problem.

f(x) = 5x2 - 2x + 3

quadratic term

linear term

constant term

5x2

-2x

3

quadratic solutions
Quadratic Solutions

The number of real solutions is at most two.

No solutions

One solution

Two solutions

solving equations
Solving Equations

When we talk about solving these equations, we want to find the value of x when y = 0. These values, where the graph crosses the x-axis, are called the x-intercepts.

These values are also referred to as solutions, zeros, or roots.

identifying solutions
Identifying Solutions

Example f(x) = x2 - 4

Solutions are -2 and 2.

identifying solutions1
Identifying Solutions

Now you try this problem.

f(x) = 2x - x2

Solutions are 0 and 2.

graphing quadratic equations
Graphing Quadratic Equations

The graph of a quadratic equation is a parabola.

The roots or zeros are the x-intercepts.

The vertex is the maximum or minimum point.

All parabolas have an axis of symmetry.

graphing quadratic equations1

x

y

0

0

1

-3

2

-4

3

-3

4

0

Graphing Quadratic Equations

One method of graphing uses a table with arbitrary

x-values.

Graph y = x2 - 4x

Roots 0 and 4 , Vertex (2, -4) ,

Axis of Symmetry x = 2

graphing quadratic equations2

x

y

-2

-1

1

3

4

Graphing Quadratic Equations

Try this problem y = x2 - 2x - 8.

Roots

Vertex

Axis of Symmetry

graphing quadratic equations3
Graphing Quadratic Equations

The graphing calculator is also a helpful tool for graphing quadratic equations.

Refer to classwork1 for directions for graphing quadratic equations on the Casio.

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