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Solving Quadratic Equation by Graphing - PowerPoint PPT Presentation

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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y = ax2 + bx + c

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)=5x2-7x+1

Linear term -7x

Constant term 1

Identifying Terms

Example f(x) = 4x2 - 3

Linear term 0

Constant term -3

Identifying Terms

Now you try this problem.

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

linear term

constant term

5x2

-2x

3

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.

Identifying Solutions

Example f(x) = x2 - 4

Solutions are -2 and 2.

Identifying Solutions

Now you try this problem.

f(x) = 2x - x2

Solutions are 0 and 2.

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.

x

y

0

0

1

-3

2

-4

3

-3

4

0

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

x

y

-2

-1

1

3

4

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

Roots

Vertex

Axis of Symmetry

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

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