Chapter 6, Sections 1 & 2 Quadratic Functions

What is a quadratic function? Definition: Where a, b, c are constants Shape of graph: Called a parabola Has a vertex point A point where the graph changes direction (x,y) Has a max or a min point Same location as vertex, only use the y value Has an axis of symmetry An imaginary line that divides the parabola into two equal parts at the vertex, written as x = # Can have 1, 2 or 0 x-intercepts Has a y-intercept

Examples – Chart handout

Types of solutions: 0 real solutions – graph does not touch the x-axis Solutions are complex and come in pairs called conjugates 1 real solution – graph touches the x-axis once This is considered to be a double root 2 real solutions – graph touches the x-axis twice

More about solutions: Finding the solution relates back to factoring The solutions can be used to write the factored form of the equation When there is a double root, the quadratic is a perfect square trinomial This means that the factors were the same If you know the solutions, you know the x-intercepts, the roots, and the zeros ALL OF THESE TERMS MEAN THE SAME THING!!!!!!

Examples– Chart from before

Your turn… Exit Slip: What are 5 things you can find from the graph of a quadratic function and explain where they are on the graph. Classwork: 6-1 in practice workbook 1-3 do part a only 4-11 as instructed