Presentation on theme: "Definitions 4/23/2017 Quadratic Equation in standard form is viewed as, ax2 + bx + c = 0, where a ≠ 0 Parabola is a u-shaped graph."— Presentation transcript:
1 Definitions4/23/2017Quadratic Equation in standard form is viewed as, ax2 + bx + c = 0, where a ≠ 0Parabola is a u-shaped graphIf a is positive, it opens upIf a is negative, it opens downVertex is the highest or lowest point of the graphAxis of Symmetry is the vertical line passing through the vertex (the “x” of vertex) it is represented by a DASHED-lineRoots/Zeros are the solutions to the Quadratic it is where the graph crosses the x-axis.Also known as the minimum or maximum value
2 Definitions4/23/2017y = x2 – 4Roots: The solutions to the equation . Also known as the zerosX-intercept(s): Point(s) where the graph crosses the x-axis.Ordered Pair: (–2, 0)Ordered Pair: (2, 0)Vertex: Minimum or maximum valueAxis of Symmetry: Line that separates the graph in half; always written asx = ______
3 To graph a Quadratic Equation 1st find the Vertexa. find the x-coordinate of the vertex by using the vertex formula.b. Substitute the x-value into the Quadratic equation to find the y-value of the vertex.Write the vertex as an ordered pair. (x, y)The x-value of the vertex ALSO gives the Axis of Symmetry.Write the Axis of Symmetry as an equation. x =__
4 2nd find the Roots…when y=0. ***where the graph crosses the x-axis***a.Set the equation = to 0b.Factor the equation.c.Solve each factor for x.
5 Example 1 Given equation: Find the vertex The x-value of vertex is: 4/23/2017Given equation:Find the vertexThe x-value of vertex is:The y-value of vertex:Vertex:Axis of symmetry:Minimum/maximum:
6 Example 1 Find the Roots Set the equation = 0 Factor the equation 4/23/2017Find the RootsSet the equation = 0Factor the equationSolve for xRoots:
7 Example 1 Vertex: Axis of symmetry: Roots: What is the Domain? Is the vertex a minimum or maximum point?Minimum at y = –9Vertex:y-intercept:Axis of symmetry:Roots:Reflection over axis of symmetryNo reflectionWhat is the Domain?What is the Range?
8 Example 2 Given equation: vertex y-coordinate Axis of symmetry Roots (y=0)1 solutionMin/max?Min at y = 0Find the y-intercept (x=0)DomainReflection over axis of symmetryRange8
9 Example 3 Given equation: vertex y-coordinate Axis of symmetry y-intercept:Given equation:Reflection over axis of symmetryvertexNo reflectiony-coordinateAxis of symmetryRoots (y=0)Min/max?Min at y = -2DomainRange
10 Your turn Given equation, y = 2x2 – 2x + 5 Determine: up How it opens 4/23/2017Given equation, y = 2x2 – 2x + 5Determine:How it opensY-InterceptThe VertexAxis of SymmetryDomainRangeMinimum/Maximumup(0, 5)(0.5, 4.5)x = 0.5All Real Numbersy > 4.5No solutionMin at 4.5