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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