Graphing Quadratic Equations from the Vertex Form

43210 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will sketch graphs of quadratics using key features and solve quadratics using the quadratic formula. - Students will be able to write, interpret and graph quadratics in vertex form. Students will be able to use the quadratic formula to solve quadratics and are able to identify some key features of a graph of a quadratic. Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal. Focus 10 Learning Goal – (HS.A-REI.B.4, HS.F-IF.B.4, HS.F-IF.C.7, HS.F-IF.C.8) = Students will sketch graphs of quadratics using key features and solve quadratics using the quadratic formula.

Graph the following three equations: y = x 2, y = (x – 2) 2 and y = (x + 2) 2  How are the graphs of these equations similar?  How are they different?  Vertex (0, 0) and (0, 2) and (0, -2)  The graphs are translations of each other. y = x 2 y = (x-2) 2 y = (x+2) 2

 Use the graphing calculator on this website and type in each of the three equations we just graphed by hand:  y = x 2  y = (x – 2) 2  y = (x + 2) 2  When you need to make the exponent, use ^ button (shift, 6)

Consider the graph of y = (x – 5) 2. Where would you expect this graph to be in relation to y = x 2 ?  We would expect this graph to be 5 units to the right of y = x 2.  Consider the graph of y = (x + 5) 2. Where would you expect this graph to be in relation to y = x 2 ?  5 units left of y = x 2.

Use the graphing website and graph the following equations:  y = x 2 +3  y= x 2 – 3  y = (x + 2) What do you notice about the vertex on each one? (0, 3) then (0, -3) then (-2, -3) Based off the equation, determine a way to find the vertex of each quadratic without using a graphing calculator or graph paper.

Without graphing, state the vertex of each quadratic: 1.y = (x – 5) (5, 3) 2.y = x 2 – (0, -2.5) 3.y = (x + 4) 2 1. (-4, 0) 4.y = (x + 9) 2 – 6 1.(-9, -6) The simplified vertex form of the quadratic equation is: y = (x – h) 2 + k, where (h, k) is the vertex.

Write a quadratic, in vertex form, whose graph will have the given vertex: 1. (1.9, -4) 1. y = (x – 1.9) 2 – 4 2. (0, 100) 1. y = x (-2, 3 / 2 ) 1. y = (x + 2) / 2

Try the following equations on the graphing calculator. Determine the effect of a leading coefficient. 1. y = (x + 2) y = -½(x + 2) y = ½(x + 2) y = 2(x + 2) y = -2(x + 2)

 The vertex is (-2, 1.5) for all five graphs.  When “ a ” the number in front of the parenthesis is between -1 and 1, the graph is wide.  When “ a ” is less than -1 or greater than 1, the graph is narrower.  What about when “ a ” is positive or negative ?

When graphing a quadratic equation in vertex form, y = a(x – h) 2 + k, (h, k) are the coordinates of the vertex.