Section 2.4

Section 2.4 PowerPoint PPT Presentation


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Section 2.4

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1. Section 2.4 Analyzing Graphs of Quadratic Functions

2. Quadratic Equation Quadratic Equation: y = ax2 + bx + c = 0 where a, b, c are constants and a 0 Second-degree equations Graph of quadratic is known as a parabola Graph is not a straight line, but the shape of a curve (Picture on the right)

3. Quadratic Function Standard Form P(x) = ax2 + bx + c expressed in . . . Standard Form P(x) = a(x – h)2 + k (a 0) Vertex of parabola = (h, k) Vertex- the point at which the graph turns (the highest or lowest point of the parabola) x=h is the axis of symmetry a > 0 parabola opens up (Vertex is lowest point) a < 0 parabola opens down (Vertex is highest point)

4. Parabola Parabolas are symmetric. Axis of Symmetry-The line through the vertex about which the parabola is symmetric.

5. Minimum or maximum values of a function occur at the VERTEX. P(x) = a(x – h)2 + k Vertex of parabola = (h, k) a > 0 parabola opens up (h,k) = minimum point Minimum Value of function is P(h)=k a < 0 parabola opens down (h,k)=maximum point Maximum Value of function is P(h)=k Minimum/Maximum values are based on y-values

6. Vertex Formula P(x) = ax2 + bx + c (a 0) The following formula will give you the x-value for the vertex of a quadratic: X= Coordinates of vertex:

7. To Graph a Quadratic Function Find the coordinates of the vertex. (Use the vertex formula.) Determine which way parabola opens by looking at a. a > 0 parabola opens up (Vertex is lowest point) a < 0 parabola opens down (Vertex is highest point) Find the x-intercept(s). (Set y = 0) Find the y-intercept. (Set x = 0) Graph additional points if needed by t-chart or symmetry.

8. Height of a Propelled Object An important application of quadratic functions deals with the height of a propelled object as a function of time elapsed after it is propelled. If air resistance is neglected, the height s (in feet) of an object propelled directly upward from an initial height s feet with initial velocity v feet per second is: s(t) = -16t² + v t + s

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