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Solving Quadratic Equation by GraphingPowerPoint Presentation

Solving Quadratic Equation by Graphing

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Solving Quadratic Equation by Graphing

Section 6.1

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

Now you try this problem.

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

quadratic term

linear term

constant term

5x2

-2x

3

Quadratic Solutions

The number of real solutions is at most two.

No solutions

One solution

Two solutions

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.

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.

y

0

0

1

-3

2

-4

3

-3

4

0

Graphing Quadratic EquationsOne 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

y

-2

-1

1

3

4

Graphing Quadratic EquationsTry this problem y = x2 - 2x - 8.

Roots

Vertex

Axis of Symmetry

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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