Graphing Quadratic Equations Day 1: Hey, this isn’t so bad

Graphs look like: y = mx +b is a ____________ Line y = |x| is a ______________ V-shape y = ax2 + bx + c is a ___________ Parabola What’s that? It’s a U-shape

To get the hang of things, let’s use a t-chart Graph y = x2 – 6x + 9 So how do we graph this? To get the hang of things, let’s use a t-chart Graph y = x2 – 6x + 9 x | y

Symmetry Parabolas are always symmetrical So what? This is because of the x being squared – because where the pattern might otherwise have gone negative, it gets squared, which makes it positive. So what? Depending on the situation, you may be interested in different parts of the graph. Height of projectiles An easy way to find the line of symmetry: x = (r1 + r2)/2 Where the “r” are the roots

Application Suppose you have a rectangle whose long side is twice the length of the short side. First of all, how many rectangles are there that fit that criteria? Provide the area of the rectangle as a function of the length of the long side. The graph we get of this function represents every possible rectangle that meets this criteria.