lesson 5.2 honors 2
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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
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