Section 2.4

Analyzing Graphs of Quadratic Functions

Quadratic EquationQuadratic 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

Parabola• Parabolas are

symmetric.

• Axis of Symmetry-The line through the vertex about which the parabola is symmetric.

Minimum or maximum values of a function occur at the VERTEX.

P(x) = a(x – h)2 + kVertex 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

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:

2

ba

2 2

b b,P

a a

To Graph a Quadratic Function

1. Find the coordinates of the vertex. (Use the vertex formula.)

2. 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)

3. Find the x-intercept(s). (Set y = 0)

4. Find the y-intercept. (Set x = 0)

2. Graph additional points if needed by t-chart or symmetry.