CHAPTER 6 SECTION 1 GRAPHING QUADRATIC FUNCTIONS

What is a Quadratic Function A Quadratic function is any function where the degree of the equation is 2.

Components of a Quadratic Function y = ax2 + bx + c ax2 = quadratic term bx = linear term c = constant

Graph of a Quadratic Function is a Parabola

What do the parts tell us? Axis of Symmetry – splits graph vertically into 2 mirrored halves. Vertex – Midpoint of graph, lies on the axis of symmetry, and is the Maximum or Minimum of the graph. Intercepts – c is the y-intercept and the graph may cross the x-axis 2, 1, or no times

Axis of Symmetry Standard Form of a quadratic. Axis of Symmetry is, ,also give you the x coordinate of the vertex. Substitute x value into equation to find the y coordinate of the vertex.

Graphing with Tables x f(x) y 2 #’s Left 1 # left 1 # right 2 #’s Right

Minimum & Maximum y – coordinate of the Vertex. a is negative Minimum a is Positive

Try: State the direction of opening and whether the graph has a minimum or a maximum Up; Minimum Down; Maximum

Find: a.) The y-intercept, the equation for the axis of symmetry, and the x-coordinate of the vertex. y = -x2 + 4x – 1 a = -1, b = 4, c = -1 y-intercept = c (the constant) c = -1 y-intercept = -1 Equation for axis of symmetry x-coordinate of vertex (Same as axis of symmetry) x-coordinate is 2.

Find: b) Make a table of values that includes the vertex. f(x) y -(0)2 + 4(0) – 1= -1 1 -(1)2 + 4(1) – 1= 2 -(2)2 + 4(2) – 1= 3 -(3)2 + 4(3) – 1= 4 -(4)2 + 4(4) – 1=

c) Graph the Function