5.8: Modeling with Quadratic Functions Objectives: Students will be able to… Write a quadratic function from its graph given a point and the vertex Write.

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5.8: Modeling with Quadratic Functions Objectives: Students will be able to… Write a quadratic function from its graph given a point and the vertex Write a quadratic function using the intercepts Use a graphing calculator to find a quadratic model for data

 VERTEX FORM: y = a (x- h) 2 + k  Vertex (h, k) = (-2, 1)  Point (x,y) = (1, -1) 1.Substitute values for x, y, h and k into the vertex form: 2.Simplify; solve for ‘a’: 3.Write the equation using a, h, and k: Write a quadratic function in vertex form with a vertex of (-2, 1) passing through the point (1, -1).

Write a quadratic function in vertex form with a vertex of (-2, 1) passing through the point (1, 10).

 INTERCEPT FORM: y = a (x – p) (x – q)  p and q are the intercepts  p= 1; q = 4  Point (x,y) = (2, -6) 1.Substitute values for p, q,x and y into the intercept form: 2.Simplify; solve for ‘a’: 3.Write the equation using a, p, and q: Write a quadratic function in intercept form with x-intercepts at x = 1 and x = 4 passing through point (2, -6).

Write a quadratic function in intercept form with x-intercepts at x = -1 and x = -4 passing through point (3, 28).

To Enter Your Data Points in Your Calculator:  STAT EDIT  Enter x values in L1 and y values in L2  Make sure the entries match up. You may need to clear your lists first. Arrow up to L1 or L2 and press CLEAR, ENTER. Do not hit DEL!!! It will delete the entire list To Graph your data:  2nd Y=  Turn STAT PLOT on  Be sure to clear any functions you have in Y= before you begin  GRAPH in an appropriate window Using a graphing calculator to create a quadratic model in Standard Form: y = ax 2 + bx + c

To Write a Quadratic Model in Standard Form (Quadratic Regression):  STAT CALC 5:QuadReg ENTER  Write the values for a, b and c in y = ax 2 + bx +c To Graph your Quadratic Regression Model:  Y= VARS 5:STATISTICS EQ 1:RegEQ  Graph  Make sure you have created a quadratic regression equation firsts before you go to graph it.

Write a quadratic function in standard form whose graph passes through the points (-1,4), (0,5), and (1,8).