Bellwork: Homework Check Algebra II

Modeling with Quadratic Functions 2.4 Modeling with Quadratic Functions Algebra II

Use the graphing calculator to make a scatter plot of the data. Algebra II

Is it a quadratic or linear model? Explain. Algebra II

Use the quadratic regression feature to find a quadratic model. Algebra II

Graph the quadratic function on the same screen as the scatter plot to verify that it fits the data. Algebra II

When does the wrench hit the ground? Explain. Algebra II

What are some real-life situations that can be modeled by quadratics. Algebra II

Modeling a quadratic function When given the vertex and a point, use vertex formula: y = a(x – h)2 + k When given the x-intercepts (zeros), use intercept form: y = a(x – p)(x – q) Algebra II

What do you have? The vertex and a point. Use vertex form. Example 1 1 Write a quadratic function from the graph. vertex: (2, -2) point: (4, 6) y = a(x – h)2 + k 6 = a (4 – 2)2 – 2 6 = a(2)2 – 2 6 = 4a – 2 8 = 4a a = 2 y = 2(x – 2)2 – 2 What do you have? The vertex and a point. Use vertex form. Algebra II

What do you have? The vertex and a point. Use vertex form. Example 2 Write a quadratic function from the graph. vertex: (0, 3) point: (2, 1) y = a(x – h)2 + k 1 = a(2 – 0)2 + 3 1 = a(2)2 + 3 -2 = 4a - ½ = a y = -½(x)2 + 3 What do you have? The vertex and a point. Use vertex form. Algebra II

Example 3 y = a(x – h)2 + k 0 = a(-3 + 1)2 – 8 0 = a(-2)2 – 8 Write a quadratic function from the given information. Vertex is (-1, -8) and a point of (-3,0) *vertex is h and k and point is x and y* y = a(x – h)2 + k 0 = a(-3 + 1)2 – 8 0 = a(-2)2 – 8 0 = 4a – 8 8 = 4a a = 2 y = 2(x + 1)2 – 8 Algebra II

Example 4 y = a(x – h)2 + k 7 = a(-4 + 2)2 + 5 7 = a(-2)2 + 5 Write a quadratic function from the given information. Vertex is (-2, 5) and a point of (-4, 7) *vertex is h and k and point is x and y* y = a(x – h)2 + k 7 = a(-4 + 2)2 + 5 7 = a(-2)2 + 5 7 = 4a + 5 2 = 4a a = ½ y = ½(x + 2)2 + 5 Algebra II

What do you have? The intercepts and a point. Use intercept form. Example 5 Write a quadratic function from the graph. intercepts: (-4, 0), (6, 0) point: (1, 25) y = a(x – p)(x – q) 25 = a(1 + 4)(1 – 6) 25 = a(5)(-5) 25 = -25a a = -1 y = -(x + 4)(x – 6) What do you have? The intercepts and a point. Use intercept form. Algebra II

What do you have? The intercepts and a point. Use intercept form. Example 6 Write a quadratic function from the graph. intercepts: (-3,0), (-4, 0) point: (-3½ , -¼) y = a(x – p)(x – q) - ¼= a(-3½ + 3)(-3½ + 4) -¼ = a(-½)(½) - ¼ = - ¼ a a = 1 y = 1(x + 3)(x + 4) What do you have? The intercepts and a point. Use intercept form. Algebra II

Example 7 y = a(x – p)(x – q) 84 = a(1 + 5)(1 – 8) 84 = a(6)(-7) Write a quadratic function from the given information. Intercepts are (-5, 0) and (8, 0) and a point of (1, 84) *p and q are the intercepts and x and y are the point* y = a(x – p)(x – q) 84 = a(1 + 5)(1 – 8) 84 = a(6)(-7) 84 = -42a a = -2 y = -2(x + 5)(x – 8) Algebra II

Example 8 y = a(x – p)(x – q) 27 = a(-2 – 7)(-2 – 10) 27 = a(-9)(-12) Write a quadratic function from the given information. Intercepts are (7, 0) and (10, 0) and a point of (-2, 27) *p and q are the intercepts and x and y are the point* y = a(x – p)(x – q) 27 = a(-2 – 7)(-2 – 10) 27 = a(-9)(-12) 27 = 108a a = ¼ y = ¼(x – 7)(x – 10) Algebra II

Write a linear or quadratic function. Algebra II

Write a linear or quadratic function. Algebra II

Write a linear or quadratic function. Algebra II

Write a linear or quadratic function. Algebra II

Closure: Exit Pass Write a quadratic function in standard form with x-intercepts (4, 0) and (-2,0) that passes through point (2, -1). Write a quadratic function in standard form whose vertex is (3, -2) and passes through (1,-7). Algebra II