Algebra 2cc Section 2.7 Graph quadratic functions in various forms A quadratic function takes the form: y = ax 2 + bx + c Its graph is called a parabola. If a>0 the parabola opens up. If a<0, the parabola opens down. The x value of the vertex is found using the formula x = -b/2a The y value of the vertex is found by substituting the x value into the equation. The y intercept is the value c. The axis of symmetry is the vertical line whose equation is x = -b/2a

Find the vertex, x and y intercepts, equation of axis of symmetry, and graph. y = ½ x 2 + 2x - 1

Find the vertex, x and y intercepts, equation of axis of symmetry, and graph. y = -x 2 + 4x - 2

Find the vertex, x and y intercepts, equation of axis of symmetry, and graph. y = ½ x 2 + 3x + 6

Forms of a quadratic function Standard y = ax 2 + bx + c Vertex form y = a(x-h) 2 + k vertex is (h,k) Y intercept is found by substituting zero in for x.

Find the vertex, x and y intercepts, axis of symmetry, and graph. y = -1/2 (x-3) 2 + 4

Find the vertex, x and y intercepts, axis of symmetry, and graph. y = 2(x+4) 2 - 3

Convert to vertex form by completing the square. Find the x and y intercepts, vertex, and graph y = x 2 + 6x + 2

Researchers conducted an experiment to determine temperatures at which people feel comfortable. The percent y of test subjects who felt comfortable at temperature x can be modeled by: y = x x – What temperature made the greatest percent of people comfortable? At this temperature, what percent felt comfortable?

The number of bacteria in a refrigerated food is given by N(t) = 20t 2 – 20t where -2 < t < 14 and where T is the temperature of the food in Celsius. At what temperature will the number of bacteria be minimal? What is the minimum number of bacteria?

The height, h, in feet of an object above the ground is given by h = -16t t where t is the time in seconds. Find the time it takes the object to strike the ground and find the maximum height of the object.

assignment Page 253 Problems 1-5, 18,19,20-30 even, 44, 45, 51, 52, 53