quadraticsparabola (u-shaped graph) y = ax2 y = -ax2 Sketching Quadratic Functions A.) Opens up or down: 1.) When "a" is positive, the graph curves upwards 2.) When "a" is negative the graph curves downward 3.) As "a" gets bigger the parabola gets thinner

B.)Vertex: 1.) The miximum or minimum point of the parabola 2.) The x- coordinate of the vertex is Max Min 3.) Find the y-coordinate by plugging in the x- value into the equation 4.) Equations in the form y = ax2 (No b or c) will always have the vertex at the origin (0,0). 5.) You must label the vertex on your graph x =

C.) Line of Symmetry 1.) Every parabola is symmetrical 2.) line of symmetry is a vertical line that cuts through the vertex and divides the curve into two symmetrical parts 3.) Points 2 and 3 will have the same y-coordinate Point 4 and 5 will have the same y-coordinate Line of symmetry 4.) Formula for finding the line of symmetry; 5.) You must draw in a dotted line for the line of symmetry x =

Answer the following questions about each quadratic equation. ex 1: y = 4x2 opens: up or down vertex: Axis of symmetry:

ex 2: y = 2x2 - 10x opens: up or down vertex: Axis of symmetry:

ex 3: y = -x2 - 8x + 32 opens: up or down vertex: Axis of symmetry:

Sketching Quadratic Functions To sketch the graph 1.) Find the vertex (the point it changes direction) 2.) Find the line of symmetry 3.) Graph a.) plot the vertex b.) Set up a table of values with two points on each side of vertex- plot the points c.) sketch the parabola

y = x2

y = -x2

y = 2x2- 4x

ex 1: y = x2 + 2x - 4