12.4 Quadratic Functions Goal: Graph Quadratic functions -A Quadratic function is a polynomial with a degree of 2

Steps to Graph a Quadratic Find the axis of symmetry x = -b/2a given f(x) =ax²+bx +c Draw your axis of symmetry as a dotted vertical line on your graph Plug in the x value of your axis of symmetry to your quadratic equation to get your corresponding y-value to make a (x,y) The (x,y) is your vertex (max or min point) Your graph of a quadratic will always be a parabola (U) If there is a negative number in front of your x² then the parabola is upside down…if it is positive then it is up To see how wide the parabola is you can either solve for the x-intercepts by factoring and setting the factors equal to zero Or make a xy table: pick 2 x- values to the left of the vertex and 2 x-values to the right of the vertex plug them into your function to get your corresponding y-values and graph your (x, y)

Steps to finding the x-intercepts (roots) of a function Set function =0 Factor Set each factor =0 Solve for your variable

Find the x-intercepts of f(x) = x2 – 5x + 6 Set the function = zero and solve.

Axis of Symmetry Parabola Model Graph Vertex

Axis of Symmetry Vertex Model graph Parabola

Graph A = -2 B = +4 C = 1

Graph x y 3 -5 2 1 -1 x y 3 2 1 -1 Axis of symmetry is x= 1 Vertex: y= -2(1)² + 4(1) +1 y= -2 +4+1 y = 3 Vertex : (1, 3) x y 3 -5 2 1 -1 x y 3 2 1 -1 X-intercepts 0 = -2x² +4 +1 0= not factorable as of now so use a xy chart

Domain is all real numbers Graph x y 3 -5 2 1 -1 x y 3 2 1 -1 Domain is all real numbers Range: { y | y }

Graph x y 3 2 -3 1 -4 -1 x y 3 2 1 -1 Range: { y | y } x - intercepts

x y 2 4 -1 4.5 -2 -4

x y

Assignment Page 554 (2-22) even and (29-31) all