Presentation on theme: "Solving Quadratic Equation by Graphing"— Presentation transcript:
1 Solving Quadratic Equation by Graphing Section 6.1 and 6.2
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.
3 Identifying Terms Example f(x)=5x2-7x+1 Quadratic term 5x2 Linear term xConstant term 1
4 Identifying Terms Example f(x) = 4x2 - 3 Quadratic term 4x2 Linear termConstant term
5 Identifying Terms Now you try this problem. f(x) = 5x2 - 2x + 3 quadratic termlinear termconstant term5x2-2x3
6 Quadratic Solutions The number of real solutions is at most two. No real solutions2 imaginary solutions (use quadratic formula or completing square to find)One solutionTwo solutionsEither 2 rational or 2 irrational (may need to use quadratic formula or completing the square to find)
7 Solving EquationsWhen 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.
8 Identifying Solutions Example f(x) = x2 - 4Solutions are -2 and 2.
9 Identifying Solutions Now you try this problem.f(x) = 2x - x2Solutions are 0 and 2.
10 Graphing Quadratic Equations 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)
11 Graphing Quadratic Equations One method of graphing uses a table with arbitraryx-values.Graph y = x2 - 4xRoots 0 and 4 , Vertex (2, -4) ,Axis of Symmetry x = 2 , y-intercept (0, 0)xy1-32-434
12 Graphing Quadratic Equations Try this problem y = x2 - 2x - 8.RootsVertexAxis of SymmetryY-interceptxy-2-1134
13 Graphing Quadratic Equations The graphing calculator is also a helpful tool for graphing quadratic equations.Enter equation into y1 and 0 in for y2To find min/max – 2nd trace min or max (also known as the vertex)To find roots – 2nd trace intersect and find where it crosses the x-axis.