 # Solving Quadratic Equation by Graphing

## Presentation on theme: "Solving Quadratic Equation by Graphing"— Presentation transcript:

Section 6.1 and 6.2

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.

Identifying Terms Example f(x)=5x2-7x+1 Quadratic term 5x2
Linear term x Constant term 1

Identifying Terms Example f(x) = 4x2 - 3 Quadratic term 4x2
Linear term Constant term

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 real solutions 2 imaginary solutions (use quadratic formula or completing square to find) One solution Two solutions Either 2 rational or 2 irrational (may need to use quadratic formula or completing the square to find)

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 (a + min, a – max) The roots or zeros are the x-intercepts. The vertex is the maximum or minimum point. All parabolas have an axis of symmetry. (x = -b/2a) Y-intercept = c (0, c)

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 , y-intercept (0, 0) x y 1 -3 2 -4 3 4