Lesson 5.2 honors 2

Solving Quadratic Equation

by Graphing

Lesson 5.2

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.

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

Quadratic term 5x2

Linear term -7x Constant term 1

Identifying Terms

Example f(x) = 4x2 - 3

Quadratic term 4x2

Linear term 0Constant term -3

Identifying Terms

Now you try this problem.

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

quadratic term linear term constant term

Identifying Terms

5x2

-2x

3

The number of real solutions is at most two.

Quadratic Solutions

No solutions

6

4

2

-2

5

f x = x2-2 x +5

6

4

2

-2

5

2

-2

-4

-5 5

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.

Example f(x) = x2 - 4

Identifying Solutions4

2

-2

-4

-5 5

Solutions are -2 and 2.

Now you try this problem.

f(x) = 2x - x2

Solutions are 0 and 2.

Identifying Solutions

4

2

-2

-4

5

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 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 Equations

x y0 01 -32 -43 -34 0

4

2

-2

-4

5

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

RootsVertexAxis of Symmetry

Graphing Quadratic Equations

x y-2-1134

4

2

-2

-4

5

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

Graphing Quadratic Equations