Presentation on theme: "Graphing Quadratic Equations in Vertex and Intercept Form"— Presentation transcript:
1 Graphing Quadratic Equations in Vertex and Intercept Form Section 4.2GraphingQuadratic Equations in Vertex and Intercept Form
2 The y intercept of the graph is c if the equation is in STANDARD FORM Quadratic FunctionsA quadratic function has the form: f (x) = ax2 + bx + cWhere a, b and c are real numbers anda is not equal to 0.The y intercept of the graph is c if the equation is in STANDARD FORM.The basic shape of the graph is a PARABOLAor U shaped
3 Positive QuadraticNegative Quadraticy = ax2y = -ax2Parabolas always have a lowest point (minimum) or a highest point (maximum, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex".
4 Vertex- Axis of symmetry- The lowest or highest point of a parabola. The vertical line through the vertex of the parabola.Axis ofSymmetry
5 Vertex Form: y = a(x – h)2 + k, - the vertex is the point (h, k). - the axis of symmetry is x = h- if “a” is positive it opens up- if “a” is negative it opens downPlot the vertex and then find two other points by using “a” as your rise/run
7 Vertex Form (x – h)2 + k – vertex form Each function we just looked at can be written in the form (x – h)2 + k, where (h , k) is the vertex of the parabola, and x = h is its axis of symmetry.(x – h)2 + k – vertex formEquationVertexAxis of Symmetryy = x2 or y = (x – 0)2 + 0(0 , 0)x = 0y = x2 + 2 or y = (x – 0)2 + 2(0 , 2)y = (x – 3)2 or y = (x – 3)2 + 0(3 , 0)x = 3
8 (-2, 5) EXAMPLE A Graph a quadratic function in vertex form 12 Graph y = – (x + 2)2 + 5.SOLUTIONSTEP 1: Identify the vertex(-2, 5)STEP 2: Plot the vertex & drawthe line of symmetrySTEP 3: Determine if it opens up or down
9 EXAMPLE AGraph a quadratic function in vertex form12Graph y = – (x + 2)2 + 5.STEP 4: Use “a” as your rise/runDown 1 and over 2STEP 5: Draw a parabola
12 Example B: Graph y = (x + 2)2 + 1 Analyze y = (x + 2)2 + 1.Step 1 Plot the vertex (-2 , 1)Step 2 Draw the axis of symmetry, x = -2.Step 3 Find and plot two points on one side , such as (-1, 2) and (0 , 5).Step 4 Use symmetry to complete the graph, or find two points on theleft side of the vertex.
13 Example C: Graph y=-.5(x+3)2+4 a is negative (a = -.5), so parabola opens down.Vertex is (h,k) or (-3,4)Axis of symmetry is the vertical line x = -3Table of values x y-1 2-3 4-5 2Vertex (-3,4)(-4,3.5)(-2,3.5)(-5,2)(-1,2)x=-3
15 Minimum “a” is positive Maximum “a” is negative GUIDED PRACTICEfor Examples 1 and 2Graph the function. Label the vertex and axis of symmetry.y = (x + 2)2 – 3Minimum “a” is positivey = –(x + 1)2 + 5Maximum “a” is negative
20 Intercept Form Equation y=a(x-p)(x-q)The x-intercepts are the points (p,0) and (q,0).The axis of symmetry is the vertical line x=The x-coordinate of the vertex isTo find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y.If “a” is positive, parabola opens upIf “a” is negative, parabola opens down.
22 Example D: Graph y=-(x+2)(x-4) Since a is negative, parabola opens down.The x-intercepts are(-2,0) and (4,0)To find the x-coord. of the vertex, useTo find the y-coord., plug 1 in for x.Vertex (1,9)The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex)(1,9)(-2,0)(4,0)x=1